diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 901095c..f9708af 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-26T01:24:36","documenter_version":"1.4.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-03T01:25:15","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/dev/DeepBSDE/index.html b/dev/DeepBSDE/index.html index 7879fc3..201e917 100644 --- a/dev/DeepBSDE/index.html +++ b/dev/DeepBSDE/index.html @@ -64,4 +64,4 @@ trajectories_lower, maxiters_limits ) -

Returns a PIDESolution object.

Arguments:

To use SDE Algorithms use DeepBSDE

source

The general idea 💡

The DeepBSDE algorithm is similar in essence to the DeepSplitting algorithm, with the difference that it uses two neural networks to approximate both the the solution and its gradient.

References

+

Returns a PIDESolution object.

Arguments:

To use SDE Algorithms use DeepBSDE

source

The general idea 💡

The DeepBSDE algorithm is similar in essence to the DeepSplitting algorithm, with the difference that it uses two neural networks to approximate both the the solution and its gradient.

References

diff --git a/dev/DeepSplitting/index.html b/dev/DeepSplitting/index.html index ca3ac1b..633b3ea 100644 --- a/dev/DeepSplitting/index.html +++ b/dev/DeepSplitting/index.html @@ -20,4 +20,4 @@ cuda_device, verbose_rate ) -> PIDESolution{_A, _B, _C, Vector{_A1}, Vector{Any}, Nothing} where {_A, _B, _C, _A1} -

Returns a PIDESolution object.

Arguments

source

The DeepSplitting algorithm reformulates the PDE as a stochastic learning problem.

The algorithm relies on two main ideas:

The general idea 💡

Consider the PDE

\[\partial_t u(t,x) = \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x) + f(x, u(t,x)) \tag{1}\]

with initial conditions $u(0, x) = g(x)$, where $u \colon \R^d \to \R$.

Local Feynman Kac formula

DeepSplitting solves the PDE iteratively over small time intervals by using an approximate Feynman-Kac representation locally.

More specifically, considering a small time step $dt = t_{n+1} - t_n$ one has that

\[u(t_{n+1}, X_{T - t_{n+1}}) \approx \mathbb{E} \left[ f(t, X_{T - t_{n}}, u(t_{n},X_{T - t_{n}}))(t_{n+1} - t_n) + u(t_{n}, X_{T - t_{n}}) | X_{T - t_{n+1}}\right] \tag{3}.\]

One can therefore use Monte Carlo integrations to approximate the expectations

\[u(t_{n+1}, X_{T - t_{n+1}}) \approx \frac{1}{\text{batch\_size}}\sum_{j=1}^{\text{batch\_size}} \left[ u(t_{n}, X_{T - t_{n}}^{(j)}) + (t_{n+1} - t_n)\sum_{k=1}^{K} \big[ f(t_n, X_{T - t_{n}}^{(j)}, u(t_{n},X_{T - t_{n}}^{(j)})) \big] \right]\]

Reformulation as a learning problem

The DeepSplitting algorithm approximates $u(t_{n+1}, x)$ by a parametric function ${\bf u}^\theta_n(x)$. It is advised to let this function be a neural network ${\bf u}_\theta \equiv NN_\theta$ as they are universal approximators.

For each time step $t_n$, the DeepSplitting algorithm

  1. Generates the particle trajectories $X^{x, (j)}$ satisfying Eq. (2) over the whole interval $[0,T]$.

  2. Seeks ${\bf u}_{n+1}^{\theta}$ by minimizing the loss function

\[L(\theta) = ||{\bf u}^\theta_{n+1}(X_{T - t_n}) - \left[ f(t, X_{T - t_{n-1}}, {\bf u}_{n-1}(X_{T - t_{n-1}}))(t_{n} - t_{n-1}) + {\bf u}_{n-1}(X_{T - t_{n-1}}) \right] ||\]

This way, the PDE approximation problem is decomposed into a sequence of separate learning problems. In HighDimPDE.jl the right parameter combination $\theta$ is found by iteratively minimizing $L$ using stochastic gradient descent.

Tip

To solve with DeepSplitting, one needs to provide to solve

Solving point-wise or on a hypercube

Pointwise

DeepSplitting allows obtaining $u(t,x)$ on a single point $x \in \Omega$ with the keyword $x$.

prob = PIDEProblem(μ, σ, x, tspan, g, f,)

Hypercube

Yet more generally, one wants to solve Eq. (1) on a $d$-dimensional cube $[a,b]^d$. This is offered by HighDimPDE.jl with the keyword x0_sample.

prob = PIDEProblem(μ, σ, x, tspan, g, f; x0_sample = x0_sample)

Internally, this is handled by assigning a random variable as the initial point of the particles, i.e.

\[X_t^\xi = \int_0^t \mu(X_s^x)ds + \int_0^t\sigma(X_s^x)dB_s + \xi,\]

where $\xi$ a random variable uniformly distributed over $[a,b]^d$. This way, the neural network is trained on the whole interval $[a,b]^d$ instead of a single point.

Non-local PDEs

DeepSplitting can solve for non-local reaction diffusion equations of the type

\[\partial_t u = \mu(x) \nabla_x u + \frac{1}{2} \sigma^2(x) \Delta u + \int_{\Omega}f(x,y, u(t,x), u(t,y))dy\]

The non-localness is handled by a Monte Carlo integration.

\[u(t_{n+1}, X_{T - t_{n+1}}) \approx \sum_{j=1}^{\text{batch\_size}} \left[ u(t_{n}, X_{T - t_{n}}^{(j)}) + \frac{(t_{n+1} - t_n)}{K}\sum_{k=1}^{K} \big[ f(t, X_{T - t_{n}}^{(j)}, Y_{X_{T - t_{n}}^{(j)}}^{(k)}, u(t_{n},X_{T - t_{n}}^{(j)}), u(t_{n},Y_{X_{T - t_{n}}^{(j)}}^{(k)})) \big] \right]\]

Tip

In practice, if you have a non-local model, you need to provide the sampling method and the number $K$ of MC integration through the keywords mc_sample and K. 

alg = DeepSplitting(nn, opt = opt, mc_sample = mc_sample, K = 1)

mc_sample can be whether UniformSampling(a, b) or NormalSampling(σ_sampling, shifted).

References

+

Returns a PIDESolution object.

Arguments

source

The DeepSplitting algorithm reformulates the PDE as a stochastic learning problem.

The algorithm relies on two main ideas:

The general idea 💡

Consider the PDE

\[\partial_t u(t,x) = \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x) + f(x, u(t,x)) \tag{1}\]

with initial conditions $u(0, x) = g(x)$, where $u \colon \R^d \to \R$.

Local Feynman Kac formula

DeepSplitting solves the PDE iteratively over small time intervals by using an approximate Feynman-Kac representation locally.

More specifically, considering a small time step $dt = t_{n+1} - t_n$ one has that

\[u(t_{n+1}, X_{T - t_{n+1}}) \approx \mathbb{E} \left[ f(t, X_{T - t_{n}}, u(t_{n},X_{T - t_{n}}))(t_{n+1} - t_n) + u(t_{n}, X_{T - t_{n}}) | X_{T - t_{n+1}}\right] \tag{3}.\]

One can therefore use Monte Carlo integrations to approximate the expectations

\[u(t_{n+1}, X_{T - t_{n+1}}) \approx \frac{1}{\text{batch\_size}}\sum_{j=1}^{\text{batch\_size}} \left[ u(t_{n}, X_{T - t_{n}}^{(j)}) + (t_{n+1} - t_n)\sum_{k=1}^{K} \big[ f(t_n, X_{T - t_{n}}^{(j)}, u(t_{n},X_{T - t_{n}}^{(j)})) \big] \right]\]

Reformulation as a learning problem

The DeepSplitting algorithm approximates $u(t_{n+1}, x)$ by a parametric function ${\bf u}^\theta_n(x)$. It is advised to let this function be a neural network ${\bf u}_\theta \equiv NN_\theta$ as they are universal approximators.

For each time step $t_n$, the DeepSplitting algorithm

  1. Generates the particle trajectories $X^{x, (j)}$ satisfying Eq. (2) over the whole interval $[0,T]$.

  2. Seeks ${\bf u}_{n+1}^{\theta}$ by minimizing the loss function

\[L(\theta) = ||{\bf u}^\theta_{n+1}(X_{T - t_n}) - \left[ f(t, X_{T - t_{n-1}}, {\bf u}_{n-1}(X_{T - t_{n-1}}))(t_{n} - t_{n-1}) + {\bf u}_{n-1}(X_{T - t_{n-1}}) \right] ||\]

This way, the PDE approximation problem is decomposed into a sequence of separate learning problems. In HighDimPDE.jl the right parameter combination $\theta$ is found by iteratively minimizing $L$ using stochastic gradient descent.

Tip

To solve with DeepSplitting, one needs to provide to solve

Solving point-wise or on a hypercube

Pointwise

DeepSplitting allows obtaining $u(t,x)$ on a single point $x \in \Omega$ with the keyword $x$.

prob = PIDEProblem(μ, σ, x, tspan, g, f,)

Hypercube

Yet more generally, one wants to solve Eq. (1) on a $d$-dimensional cube $[a,b]^d$. This is offered by HighDimPDE.jl with the keyword x0_sample.

prob = PIDEProblem(μ, σ, x, tspan, g, f; x0_sample = x0_sample)

Internally, this is handled by assigning a random variable as the initial point of the particles, i.e.

\[X_t^\xi = \int_0^t \mu(X_s^x)ds + \int_0^t\sigma(X_s^x)dB_s + \xi,\]

where $\xi$ a random variable uniformly distributed over $[a,b]^d$. This way, the neural network is trained on the whole interval $[a,b]^d$ instead of a single point.

Non-local PDEs

DeepSplitting can solve for non-local reaction diffusion equations of the type

\[\partial_t u = \mu(x) \nabla_x u + \frac{1}{2} \sigma^2(x) \Delta u + \int_{\Omega}f(x,y, u(t,x), u(t,y))dy\]

The non-localness is handled by a Monte Carlo integration.

\[u(t_{n+1}, X_{T - t_{n+1}}) \approx \sum_{j=1}^{\text{batch\_size}} \left[ u(t_{n}, X_{T - t_{n}}^{(j)}) + \frac{(t_{n+1} - t_n)}{K}\sum_{k=1}^{K} \big[ f(t, X_{T - t_{n}}^{(j)}, Y_{X_{T - t_{n}}^{(j)}}^{(k)}, u(t_{n},X_{T - t_{n}}^{(j)}), u(t_{n},Y_{X_{T - t_{n}}^{(j)}}^{(k)})) \big] \right]\]

Tip

In practice, if you have a non-local model, you need to provide the sampling method and the number $K$ of MC integration through the keywords mc_sample and K. 

alg = DeepSplitting(nn, opt = opt, mc_sample = mc_sample, K = 1)

mc_sample can be whether UniformSampling(a, b) or NormalSampling(σ_sampling, shifted).

References

diff --git a/dev/Feynman_Kac/index.html b/dev/Feynman_Kac/index.html index 8028276..a8abc2c 100644 --- a/dev/Feynman_Kac/index.html +++ b/dev/Feynman_Kac/index.html @@ -7,4 +7,4 @@ v(\tau, x) &= \int_{-\tau}^0 \mathbb{E} \left[ f(X^x_{s + \tau}, v(s + T, X^x_{s + \tau}))ds \right] + \mathbb{E} \left[ v(0, X^x_{\tau}) \right]\\ &= - \int_{\tau}^0 \mathbb{E} \left[ f(X^x_{\tau - s}, v(T-s, X^x_{\tau - s}))ds \right] + \mathbb{E} \left[ v(0, X^x_{\tau}) \right]\\ &= \int_{0}^\tau \mathbb{E} \left[ f(X^x_{\tau - s}, v(T-s, X^x_{\tau - s}))ds \right] + \mathbb{E} \left[ v(0, X^x_{\tau}) \right]. -\end{aligned}\]

This leads to the

Non-linear Feynman Kac for initial value problems

Consider the PDE

\[\partial_t u(t,x) = \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x) + f(x, u(t,x))\]

with initial conditions $u(0, x) = g(x)$, where $u \colon \R^d \to \R$. Then

\[u(t, x) = \int_0^t \mathbb{E} \left[ f(X^x_{t - s}, u(T-s, X^x_{t - s}))ds \right] + \mathbb{E} \left[ u(0, X^x_t) \right] \tag{3}\]

with

\[X_t^x = \int_0^t \mu(X_s^x)ds + \int_0^t\sigma(X_s^x)dB_s + x.\]

+\end{aligned}\]

This leads to the

Non-linear Feynman Kac for initial value problems

Consider the PDE

\[\partial_t u(t,x) = \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x) + f(x, u(t,x))\]

with initial conditions $u(0, x) = g(x)$, where $u \colon \R^d \to \R$. Then

\[u(t, x) = \int_0^t \mathbb{E} \left[ f(X^x_{t - s}, u(T-s, X^x_{t - s}))ds \right] + \mathbb{E} \left[ u(0, X^x_t) \right] \tag{3}\]

with

\[X_t^x = \int_0^t \mu(X_s^x)ds + \int_0^t\sigma(X_s^x)dB_s + x.\]

diff --git a/dev/MLP/index.html b/dev/MLP/index.html index d5c038e..0a787ae 100644 --- a/dev/MLP/index.html +++ b/dev/MLP/index.html @@ -16,4 +16,4 @@ u_L &= \sum_{l=1}^{L-1} \frac{1}{M^{L-l}}\sum_{i=1}^{M^{L-l}} \frac{1}{K}\sum_{j=1}^{K} \bigg[ f(X^{x,(l, i)}_{t - s_{(l, i)}}, Z^{(l,j)}, u(T-s_{(l, i)}, X^{x,(l, i)}_{t - s_{(l, i)}}), u(T-s_{l,i}, Z^{(l,j)})) + \\ &\qquad \mathbf{1}_\N(l) f(X^{x,(l, i)}_{t - s_{(l, i)}}, u(T-s_{(l, i)}, X^{x,(l, i)}_{t - s_{(l, i)}}))\bigg] + \frac{1}{M^{L}}\sum_i^{M^{L}} u(0, X^{x,(l, i)}_t)\\ -\end{aligned}\]

Tip

In practice, if you have a non-local model, you need to provide the sampling method and the number $K$ of MC integration through the keywords mc_sample and K.

References

+\end{aligned}\]

Tip

In practice, if you have a non-local model, you need to provide the sampling method and the number $K$ of MC integration through the keywords mc_sample and K.

References

diff --git a/dev/NNKolmogorov/index.html b/dev/NNKolmogorov/index.html index 8044934..98dcfb5 100644 --- a/dev/NNKolmogorov/index.html +++ b/dev/NNKolmogorov/index.html @@ -14,4 +14,4 @@ dx, kwargs... ) -

Returns a PIDESolution object.

Arguments

source

NNKolmogorov obtains a

\[\partial_t u(t,x) = \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x)\]

with initial condition given by g(x)

\[\partial_t u(t,x) = - \mu(t, x) \nabla_x u(t,x) - \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x)\]

with terminal condition given by g(x)

We can use the Feynman-Kac formula :

\[S_t^x = \int_{0}^{t}\mu(S_s^x)ds + \int_{0}^{t}\sigma(S_s^x)dB_s\]

And the solution is given by:

\[f(T, x) = \mathbb{E}[g(S_T^x)]\]

+

Returns a PIDESolution object.

Arguments

source

NNKolmogorov obtains a

\[\partial_t u(t,x) = \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x)\]

with initial condition given by g(x)

\[\partial_t u(t,x) = - \mu(t, x) \nabla_x u(t,x) - \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x)\]

with terminal condition given by g(x)

We can use the Feynman-Kac formula :

\[S_t^x = \int_{0}^{t}\mu(S_s^x)ds + \int_{0}^{t}\sigma(S_s^x)dB_s\]

And the solution is given by:

\[f(T, x) = \mathbb{E}[g(S_T^x)]\]

diff --git a/dev/NNParamKolmogorov/index.html b/dev/NNParamKolmogorov/index.html index 78a4a6d..1d16f8f 100644 --- a/dev/NNParamKolmogorov/index.html +++ b/dev/NNParamKolmogorov/index.html @@ -20,4 +20,4 @@ dx, kwargs... ) -

Returns a PIDESolution object.

Arguments

source

NNParamKolmogorov obtains a

\[\partial_t u(t,x) = \mu(t, x, γ_mu) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x, γ_sigma) \Delta_x u(t,x)\]

with initial condition given by g(x, γ_phi)

\[\partial_t u(t,x) = - \mu(t, x) \nabla_x u(t,x) - \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x)\]

with terminal condition given by g(x, γ_phi)

We can use the Feynman-Kac formula :

\[S_t^x = \int_{0}^{t}\mu(S_s^x)ds + \int_{0}^{t}\sigma(S_s^x)dB_s\]

And the solution is given by:

\[f(T, x) = \mathbb{E}[g(S_T^x, γ_phi)]\]

+

Returns a PIDESolution object.

Arguments

source

NNParamKolmogorov obtains a

\[\partial_t u(t,x) = \mu(t, x, γ_mu) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x, γ_sigma) \Delta_x u(t,x)\]

with initial condition given by g(x, γ_phi)

\[\partial_t u(t,x) = - \mu(t, x) \nabla_x u(t,x) - \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x)\]

with terminal condition given by g(x, γ_phi)

We can use the Feynman-Kac formula :

\[S_t^x = \int_{0}^{t}\mu(S_s^x)ds + \int_{0}^{t}\sigma(S_s^x)dB_s\]

And the solution is given by:

\[f(T, x) = \mathbb{E}[g(S_T^x, γ_phi)]\]

diff --git a/dev/NNStopping/index.html b/dev/NNStopping/index.html index 3cb0894..a5cd771 100644 --- a/dev/NNStopping/index.html +++ b/dev/NNStopping/index.html @@ -10,4 +10,4 @@ ensemblealg, kwargs... ) -> NamedTuple{(:payoff, :stopping_time), <:Tuple{Any, Any}} -

Returns a NamedTuple with payoff and stopping_time

Arguments:

source

The general idea 💡

Similar to DeepSplitting and DeepBSDE, NNStopping evaluates the PDE as a Stochastic Differential Equation. Consider an Obstacle PDE of the form:

\[ max\lbrace\partial_t u(t,x) + \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x) , g(t,x) - u(t,x)\rbrace\]

Such PDEs are commonly used as representations for the dynamics of stock prices that can be exercised before maturity, such as American Options.

Using the Feynman-Kac formula, the underlying SDE will be:

\[dX_{t}=\mu(X,t)dt + \sigma(X,t)\ dW_{t}^{Q}\]

The payoff of the option would then be:

\[sup\lbrace\mathbb{E}[g(X_\tau, \tau)]\rbrace\]

Where τ is the stopping (exercising) time. The goal is to retrieve both the optimal exercising strategy (τ) and the payoff.

We approximate each stopping decision with a neural network architecture, inorder to maximise the expected payoff.

+

Returns a NamedTuple with payoff and stopping_time

Arguments:

source

The general idea 💡

Similar to DeepSplitting and DeepBSDE, NNStopping evaluates the PDE as a Stochastic Differential Equation. Consider an Obstacle PDE of the form:

\[ max\lbrace\partial_t u(t,x) + \mu(t, x) \nabla_x u(t,x) + \frac{1}{2} \sigma^2(t, x) \Delta_x u(t,x) , g(t,x) - u(t,x)\rbrace\]

Such PDEs are commonly used as representations for the dynamics of stock prices that can be exercised before maturity, such as American Options.

Using the Feynman-Kac formula, the underlying SDE will be:

\[dX_{t}=\mu(X,t)dt + \sigma(X,t)\ dW_{t}^{Q}\]

The payoff of the option would then be:

\[sup\lbrace\mathbb{E}[g(X_\tau, \tau)]\rbrace\]

Where τ is the stopping (exercising) time. The goal is to retrieve both the optimal exercising strategy (τ) and the payoff.

We approximate each stopping decision with a neural network architecture, inorder to maximise the expected payoff.

diff --git a/dev/assets/Manifest.toml b/dev/assets/Manifest.toml index ed1a029..1e06cbb 100644 --- a/dev/assets/Manifest.toml +++ b/dev/assets/Manifest.toml @@ -1,6 +1,6 @@ # This file is machine-generated - editing it directly is not advised -julia_version = "1.10.2" +julia_version = "1.10.3" manifest_format = "2.0" project_hash = "655e215c4addc5f8a90c4adfdcef30f240ee3d6b" @@ -63,9 +63,9 @@ weakdeps = ["StaticArrays"] [[deps.AliasTables]] deps = ["Random"] -git-tree-sha1 = "ca95b2220ef440817963baa71525a8f2f4ae7f8f" +git-tree-sha1 = "07591db28451b3e45f4c0088a2d5e986ae5aa92d" uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8" -version = "1.0.0" +version = "1.1.1" [[deps.ArgCheck]] git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4" @@ -182,9 +182,9 @@ version = "0.2.4" [[deps.CUDA]] deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CUDA_Driver_jll", "CUDA_Runtime_Discovery", "CUDA_Runtime_jll", "Crayons", "DataFrames", "ExprTools", "GPUArrays", "GPUCompiler", "KernelAbstractions", "LLVM", "LLVMLoopInfo", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "NVTX", "Preferences", "PrettyTables", "Printf", "Random", "Random123", "RandomNumbers", "Reexport", "Requires", "SparseArrays", "StaticArrays", "Statistics"] -git-tree-sha1 = "dd1c682b372b6791b69f6823afe364fc92a0146c" +git-tree-sha1 = "4e33522a036b39fc6f5cb7447ae3b28eb8fbe99b" uuid = "052768ef-5323-5732-b1bb-66c8b64840ba" -version = "5.3.1" +version = "5.3.3" weakdeps = ["ChainRulesCore", "SpecialFunctions"] [deps.CUDA.extensions] @@ -290,7 +290,7 @@ weakdeps = ["Dates", "LinearAlgebra"] [[deps.CompilerSupportLibraries_jll]] deps = ["Artifacts", "Libdl"] uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" -version = "1.1.0+0" +version = "1.1.1+0" [[deps.CompositionsBase]] git-tree-sha1 = "802bb88cd69dfd1509f6670416bd4434015693ad" @@ -406,9 +406,9 @@ version = "6.149.1" [[deps.DiffEqCallbacks]] deps = ["DataStructures", "DiffEqBase", "ForwardDiff", "Functors", "LinearAlgebra", "Markdown", "NonlinearSolve", "Parameters", "RecipesBase", "RecursiveArrayTools", "SciMLBase", "StaticArraysCore"] -git-tree-sha1 = "ec436ca77daad49b71147d873638c206543c2312" +git-tree-sha1 = "c959cfd2657d16beada157a74d52269e8556500e" uuid = "459566f4-90b8-5000-8ac3-15dfb0a30def" -version = "3.6.1" +version = "3.6.2" [deps.DiffEqCallbacks.weakdeps] OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" @@ -475,9 +475,9 @@ version = "0.9.3" [[deps.Documenter]] deps = ["ANSIColoredPrinters", "AbstractTrees", "Base64", "CodecZlib", "Dates", "DocStringExtensions", "Downloads", "Git", "IOCapture", "InteractiveUtils", "JSON", "LibGit2", "Logging", "Markdown", "MarkdownAST", "Pkg", "PrecompileTools", "REPL", "RegistryInstances", "SHA", "TOML", "Test", "Unicode"] -git-tree-sha1 = "f15a91e6e3919055efa4f206f942a73fedf5dfe6" +git-tree-sha1 = "5461b2a67beb9089980e2f8f25145186b6d34f91" uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4" -version = "1.4.0" +version = "1.4.1" [[deps.Downloads]] deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] @@ -528,9 +528,9 @@ version = "0.0.102+0" [[deps.Expat_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "4558ab818dcceaab612d1bb8c19cee87eda2b83c" +git-tree-sha1 = "1c6317308b9dc757616f0b5cb379db10494443a7" uuid = "2e619515-83b5-522b-bb60-26c02a35a201" -version = "2.5.0+0" +version = "2.6.2+0" [[deps.ExponentialUtilities]] deps = ["Adapt", "ArrayInterface", "GPUArraysCore", "GenericSchur", "LinearAlgebra", "PrecompileTools", "Printf", "SparseArrays", "libblastrampoline_jll"] @@ -568,9 +568,9 @@ version = "0.3.2" [[deps.FastLapackInterface]] deps = ["LinearAlgebra"] -git-tree-sha1 = "0a59c7d1002f3131de53dc4568a47d15a44daef7" +git-tree-sha1 = "f4102aab9c7df8691ed09f9c42e34f5ab5458ab9" uuid = "29a986be-02c6-4525-aec4-84b980013641" -version = "2.0.2" +version = "2.0.3" [[deps.FileWatching]] uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" @@ -844,9 +844,9 @@ weakdeps = ["EnzymeCore"] [[deps.Krylov]] deps = ["LinearAlgebra", "Printf", "SparseArrays"] -git-tree-sha1 = "8a6837ec02fe5fb3def1abc907bb802ef11a0729" +git-tree-sha1 = "267dad6b4b7b5d529c76d40ff48d33f7e94cb834" uuid = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7" -version = "0.9.5" +version = "0.9.6" [[deps.LLVM]] deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Preferences", "Printf", "Requires", "Unicode"] @@ -950,9 +950,9 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" [[deps.LinearSolve]] deps = ["ArrayInterface", "ChainRulesCore", "ConcreteStructs", "DocStringExtensions", "EnumX", "FastLapackInterface", "GPUArraysCore", "InteractiveUtils", "KLU", "Krylov", "LazyArrays", "Libdl", "LinearAlgebra", "MKL_jll", "Markdown", "PrecompileTools", "Preferences", "RecursiveFactorization", "Reexport", "SciMLBase", "SciMLOperators", "Setfield", "SparseArrays", "Sparspak", "StaticArraysCore", "UnPack"] -git-tree-sha1 = "bdf5c9162ff9ba8b320d8bbaa076d11dcf8a6c8b" +git-tree-sha1 = "c55172df0d19b34db93c410cfcd79dbc3e52ba6f" uuid = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae" -version = "2.29.0" +version = "2.29.1" [deps.LinearSolve.extensions] LinearSolveBandedMatricesExt = "BandedMatrices" @@ -1006,9 +1006,9 @@ uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" [[deps.LoopVectorization]] deps = ["ArrayInterface", "CPUSummary", "CloseOpenIntervals", "DocStringExtensions", "HostCPUFeatures", "IfElse", "LayoutPointers", "LinearAlgebra", "OffsetArrays", "PolyesterWeave", "PrecompileTools", "SIMDTypes", "SLEEFPirates", "Static", "StaticArrayInterface", "ThreadingUtilities", "UnPack", "VectorizationBase"] -git-tree-sha1 = "a13f3be5d84b9c95465d743c82af0b094ef9c2e2" +git-tree-sha1 = "8f6786d8b2b3248d79db3ad359ce95382d5a6df8" uuid = "bdcacae8-1622-11e9-2a5c-532679323890" -version = "0.12.169" +version = "0.12.170" weakdeps = ["ChainRulesCore", "ForwardDiff", "SpecialFunctions"] [deps.LoopVectorization.extensions] @@ -1403,9 +1403,9 @@ version = "1.3.4" [[deps.RecursiveArrayTools]] deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "IteratorInterfaceExtensions", "LinearAlgebra", "RecipesBase", "SparseArrays", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"] -git-tree-sha1 = "d8f131090f2e44b145084928856a561c83f43b27" +git-tree-sha1 = "b65276455c0c52b63faeca61b02fd73287fcfdd2" uuid = "731186ca-8d62-57ce-b412-fbd966d074cd" -version = "3.13.0" +version = "3.14.0" [deps.RecursiveArrayTools.extensions] RecursiveArrayToolsFastBroadcastExt = "FastBroadcast" @@ -1495,9 +1495,9 @@ version = "0.6.42" [[deps.SciMLBase]] deps = ["ADTypes", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "PrecompileTools", "Preferences", "Printf", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLOperators", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"] -git-tree-sha1 = "beb1f94b08c4976ed1db0ca01b9e6bac89706faf" +git-tree-sha1 = "15332626b477b37fd44913dd8fa607c8c25171e6" uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462" -version = "2.35.0" +version = "2.36.0" [deps.SciMLBase.extensions] SciMLBaseChainRulesCoreExt = "ChainRulesCore" @@ -1768,10 +1768,10 @@ uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c" version = "7.2.1+1" [[deps.SymbolicIndexingInterface]] -deps = ["Accessors", "ArrayInterface", "MacroTools", "RuntimeGeneratedFunctions", "StaticArraysCore"] -git-tree-sha1 = "40ea524431a92328cd73582d1820a5b08247a40f" +deps = ["Accessors", "ArrayInterface", "RuntimeGeneratedFunctions", "StaticArraysCore"] +git-tree-sha1 = "c4e6b5ec8c8cf592032664b6f4d75a389b420f87" uuid = "2efcf032-c050-4f8e-a9bb-153293bab1f5" -version = "0.3.16" +version = "0.3.20" [[deps.TOML]] deps = ["Dates"] @@ -1892,9 +1892,9 @@ version = "0.1.3" [[deps.VectorizationBase]] deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", 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.button.is-link.is-outlined.is-focused{background-color:#1abc9c;border-color:#1abc9c;color:#fff}html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-link.is-light{background-color:#edfdf9;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:hover,html.theme--documenter-dark .button.is-link.is-light.is-hovered{background-color:#e2fbf6;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:active,html.theme--documenter-dark .button.is-link.is-light.is-active{background-color:#d7f9f3;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-info{background-color:#024c7d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:hover,html.theme--documenter-dark .button.is-info.is-hovered{background-color:#024470;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus,html.theme--documenter-dark .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus:not(:active),html.theme--documenter-dark .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(2,76,125,0.25)}html.theme--documenter-dark .button.is-info:active,html.theme--documenter-dark .button.is-info.is-active{background-color:#023d64;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info{background-color:#024c7d;border-color:#024c7d;box-shadow:none}html.theme--documenter-dark .button.is-info.is-inverted{background-color:#fff;color:#024c7d}html.theme--documenter-dark .button.is-info.is-inverted:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#024c7d}html.theme--documenter-dark .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#024c7d;color:#024c7d}html.theme--documenter-dark .button.is-info.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-outlined.is-focused{background-color:#024c7d;border-color:#024c7d;color:#fff}html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #024c7d #024c7d !important}html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#024c7d;box-shadow:none;color:#024c7d}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#024c7d}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #024c7d #024c7d !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-info.is-light{background-color:#ebf7ff;color:#0e9dfb}html.theme--documenter-dark .button.is-info.is-light:hover,html.theme--documenter-dark .button.is-info.is-light.is-hovered{background-color:#def2fe;border-color:transparent;color:#0e9dfb}html.theme--documenter-dark .button.is-info.is-light:active,html.theme--documenter-dark .button.is-info.is-light.is-active{background-color:#d2edfe;border-color:transparent;color:#0e9dfb}html.theme--documenter-dark .button.is-success{background-color:#008438;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:hover,html.theme--documenter-dark .button.is-success.is-hovered{background-color:#073;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus,html.theme--documenter-dark .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus:not(:active),html.theme--documenter-dark .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(0,132,56,0.25)}html.theme--documenter-dark .button.is-success:active,html.theme--documenter-dark .button.is-success.is-active{background-color:#006b2d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success{background-color:#008438;border-color:#008438;box-shadow:none}html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;color:#008438}html.theme--documenter-dark .button.is-success.is-inverted:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#008438}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#008438;color:#008438}html.theme--documenter-dark .button.is-success.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-outlined.is-focused{background-color:#008438;border-color:#008438;color:#fff}html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #008438 #008438 !important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#008438;box-shadow:none;color:#008438}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#008438}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #008438 #008438 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success.is-light{background-color:#ebfff3;color:#00eb64}html.theme--documenter-dark .button.is-success.is-light:hover,html.theme--documenter-dark .button.is-success.is-light.is-hovered{background-color:#deffec;border-color:transparent;color:#00eb64}html.theme--documenter-dark .button.is-success.is-light:active,html.theme--documenter-dark .button.is-success.is-light.is-active{background-color:#d1ffe5;border-color:transparent;color:#00eb64}html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning:hover,html.theme--documenter-dark .button.is-warning.is-hovered{background-color:#a07700;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning:focus,html.theme--documenter-dark .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning:focus:not(:active),html.theme--documenter-dark .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(173,129,0,0.25)}html.theme--documenter-dark .button.is-warning:active,html.theme--documenter-dark .button.is-warning.is-active{background-color:#946e00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:#ad8100;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-outlined.is-focused{background-color:#ad8100;border-color:#ad8100;color:#fff}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#92190c;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(158,27,13,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#86170b;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:#9e1b0d;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#9e1b0d;border-color:#9e1b0d;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons 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.buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark 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h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark 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kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content 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.docs-logo>img.is-5by4{padding-top:80%}html.theme--documenter-dark .image.is-4by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--documenter-dark .image.is-3by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--documenter-dark .image.is-5by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--documenter-dark .image.is-16by9,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--documenter-dark .image.is-2by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--documenter-dark .image.is-3by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar 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span.sgr42{background-color:#066f00}.ansi span.sgr43{background-color:#856b00}.ansi span.sgr44{background-color:#2149b0}.ansi span.sgr45{background-color:#7d4498}.ansi span.sgr46{background-color:#007989}.ansi span.sgr47{background-color:gray}.ansi span.sgr90{color:#616161}.ansi span.sgr91{color:#cb3c33}.ansi span.sgr92{color:#0e8300}.ansi span.sgr93{color:#a98800}.ansi span.sgr94{color:#3c5dcd}.ansi span.sgr95{color:#9256af}.ansi span.sgr96{color:#008fa3}.ansi span.sgr97{color:#f5f5f5}.ansi span.sgr100{background-color:#616161}.ansi span.sgr101{background-color:#cb3c33}.ansi span.sgr102{background-color:#0e8300}.ansi span.sgr103{background-color:#a98800}.ansi span.sgr104{background-color:#3c5dcd}.ansi span.sgr105{background-color:#9256af}.ansi span.sgr106{background-color:#008fa3}.ansi span.sgr107{background-color:#f5f5f5}code.language-julia-repl>span.hljs-meta{color:#066f00;font-weight:bolder}/*! Theme: Default Description: Original highlight.js style Author: (c) Ivan Sagalaev diff --git a/dev/getting_started/index.html b/dev/getting_started/index.html index 4cca334..09e450f 100644 --- a/dev/getting_started/index.html +++ b/dev/getting_started/index.html @@ -17,7 +17,7 @@ ## Solving with multiple threads sol = solve(prob, alg, multithreading = true)
PIDESolution
 timespan: [0.0, 0.5]
-u(x,t): [1.0, 0.9677369705299604]

Non-local PDE with Neumann boundary conditions

Let's include in the previous equation non-local competition, i.e.

\[\partial_t u = u (1 - \int_\Omega u(t,y)dy) + \frac{1}{2}\sigma^2\Delta_xu \tag{2}\]

where $\Omega = [-1/2, 1/2]^d$, and let's assume Neumann Boundary condition on $\Omega$.

using HighDimPDE
+u(x,t): [1.0, 0.972612416838198]

Non-local PDE with Neumann boundary conditions

Let's include in the previous equation non-local competition, i.e.

\[\partial_t u = u (1 - \int_\Omega u(t,y)dy) + \frac{1}{2}\sigma^2\Delta_xu \tag{2}\]

where $\Omega = [-1/2, 1/2]^d$, and let's assume Neumann Boundary condition on $\Omega$.

using HighDimPDE
 
 ## Definition of the problem
 d = 10 # dimension of the problem
@@ -35,7 +35,7 @@
 
 sol = solve(prob, alg, multithreading = true)
PIDESolution
 timespan: [0.0, 0.5]
-u(x,t): [1.0, 1.2299829946516403]

DeepSplitting

Let's solve the previous equation with DeepSplitting.

using HighDimPDE
+u(x,t): [1.0, 1.2232965683999573]

DeepSplitting

Let's solve the previous equation with DeepSplitting.

using HighDimPDE
 using Flux # needed to define the neural network
 
 ## Definition of the problem
@@ -72,11 +72,11 @@
             maxiters = 1000,
             batch_size = 1000)
PIDESolution
 timespan: 0.0:0.09999988228082657:0.49999941140413284
-u(x,t): Float32[1.0, 0.88389146, 0.9317805, 0.9684232, 1.0236336, 1.057088]

Solving on the GPU

DeepSplitting can run on the GPU for (much) improved performance. To do so, just set use_cuda = true.

sol = solve(prob, 
+u(x,t): Float32[1.0, 0.918263, 0.9654702, 1.007776, 1.0457141, 1.0868536]

Solving on the GPU

DeepSplitting can run on the GPU for (much) improved performance. To do so, just set use_cuda = true.

sol = solve(prob, 
             alg, 
             0.1, 
             verbose = true, 
             abstol = 2e-3,
             maxiters = 1000,
             batch_size = 1000,
-            use_cuda=true)
+ use_cuda=true) diff --git a/dev/index.html b/dev/index.html index 82f598f..0d41e2e 100644 --- a/dev/index.html +++ b/dev/index.html @@ -6,10 +6,10 @@ (\partial_t u)(t,x) &= f\big(t,x, u(t,x), ( \nabla_x u )(t,x )\big) + \big\langle \mu(t,x), ( \nabla_x u )( t,x ) \big\rangle + \tfrac{1}{2} \text{Trace} \big(\sigma(t,x) [ \sigma(t,x) ]^* ( \text{Hess}_x u)(t, x ) \big). \end{aligned}\]

where $u \colon [0,T] \times \Omega \to \R$, $\Omega \subseteq \R^d$ is subject to initial and boundary conditions, and where $d$ is large.

Note

The difference between the two problems is that in Partial Integro Differential Equations, the integrand is integrated over x, while in Parabolic Integro Differential Equations, the function f is just evaluated for x.

HighDimPDE.jl implements solver algorithms that break down the curse of dimensionality, including

To make the most out of HighDimPDE.jl, we advise to first have a look at the

as all solver algorithms heavily rely on it.

Algorithm overview

FeaturesDeepSplittingMLPDeepBSDE
Time discretization free❌✅❌
Mesh-free✅✅✅
Single point $x \in \R^d$ approximation✅✅✅
$d$-dimensional cube $[a,b]^d$ approximation✅❌✔️
GPU✅❌✅
Gradient non-linearities✔️❌✅

✔️ : will be supported in the future

Reproducibility

The documentation of this SciML package was built using these direct dependencies,
Status `~/work/HighDimPDE.jl/HighDimPDE.jl/docs/Project.toml`
-  [e30172f5] Documenter v1.4.0
+  [e30172f5] Documenter v1.4.1
   [587475ba] Flux v0.14.15
-  [57c578d5] HighDimPDE v2.0.0 `~/work/HighDimPDE.jl/HighDimPDE.jl`
and using this machine and Julia version.
Julia Version 1.10.2
-Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+  [57c578d5] HighDimPDE v2.0.0 `~/work/HighDimPDE.jl/HighDimPDE.jl`
and using this machine and Julia version.
Julia Version 1.10.3
+Commit 0b4590a5507 (2024-04-30 10:59 UTC)
 Build Info:
   Official https://julialang.org/ release
 Platform Info:
@@ -25,7 +25,7 @@
   [1520ce14] AbstractTrees v0.4.5
   [7d9f7c33] Accessors v0.1.36
   [79e6a3ab] Adapt v4.0.4
-  [66dad0bd] AliasTables v1.0.0
+  [66dad0bd] AliasTables v1.1.1
   [dce04be8] ArgCheck v2.3.0
   [ec485272] ArnoldiMethod v0.4.0
   [4fba245c] ArrayInterface v7.10.0
@@ -37,7 +37,7 @@
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   [fa961155] CEnum v0.5.0
   [2a0fbf3d] CPUSummary v0.2.4
-  [052768ef] CUDA v5.3.1
+  [052768ef] CUDA v5.3.3
   [1af6417a] CUDA_Runtime_Discovery v0.2.4
   [49dc2e85] Calculus v0.5.1
   [7057c7e9] Cassette v0.3.13
@@ -63,14 +63,14 @@
   [244e2a9f] DefineSingletons v0.1.2
   [8bb1440f] DelimitedFiles v1.9.1
   [2b5f629d] DiffEqBase v6.149.1
-  [459566f4] DiffEqCallbacks v3.6.1
+  [459566f4] DiffEqCallbacks v3.6.2
   [77a26b50] DiffEqNoiseProcess v5.21.0
   [163ba53b] DiffResults v1.1.0
   [b552c78f] DiffRules v1.15.1
   [b4f34e82] Distances v0.10.11
   [31c24e10] Distributions v0.25.108
   [ffbed154] DocStringExtensions v0.9.3
-  [e30172f5] Documenter v1.4.0
+  [e30172f5] Documenter v1.4.1
   [fa6b7ba4] DualNumbers v0.6.8
   [da5c29d0] EllipsisNotation v1.8.0
   [4e289a0a] EnumX v1.0.4
@@ -82,7 +82,7 @@
   [b9860ae5] FLoopsBase v0.1.1
   [7034ab61] FastBroadcast v0.2.8
   [9aa1b823] FastClosures v0.3.2
-  [29a986be] FastLapackInterface v2.0.2
+  [29a986be] FastLapackInterface v2.0.3
   [1a297f60] FillArrays v1.10.2
   [6a86dc24] FiniteDiff v2.23.1
   [53c48c17] FixedPointNumbers v0.8.4
@@ -117,7 +117,7 @@
   [ccbc3e58] JumpProcesses v9.11.1
   [ef3ab10e] KLU v0.6.0
   [63c18a36] KernelAbstractions v0.9.18
-  [ba0b0d4f] Krylov v0.9.5
+  [ba0b0d4f] Krylov v0.9.6
   [929cbde3] LLVM v6.6.3
   [8b046642] LLVMLoopInfo v1.0.0
   [b964fa9f] LaTeXStrings v1.3.1
@@ -126,9 +126,9 @@
   [5078a376] LazyArrays v1.10.0
   [2d8b4e74] LevyArea v1.0.0
   [d3d80556] LineSearches v7.2.0
-  [7ed4a6bd] LinearSolve v2.29.0
+  [7ed4a6bd] LinearSolve v2.29.1
   [2ab3a3ac] LogExpFunctions v0.3.27
-  [bdcacae8] LoopVectorization v0.12.169
+  [bdcacae8] LoopVectorization v0.12.170
   [d8e11817] MLStyle v0.4.17
   [f1d291b0] MLUtils v0.4.4
   [1914dd2f] MacroTools v0.5.13
@@ -173,7 +173,7 @@
   [e6cf234a] RandomNumbers v1.5.3
   [c1ae055f] RealDot v0.1.0
   [3cdcf5f2] RecipesBase v1.3.4
-  [731186ca] RecursiveArrayTools v3.13.0
+  [731186ca] RecursiveArrayTools v3.14.0
   [f2c3362d] RecursiveFactorization v0.2.23
   [189a3867] Reexport v1.2.2
   [2792f1a3] RegistryInstances v0.1.0
@@ -184,7 +184,7 @@
   [7e49a35a] RuntimeGeneratedFunctions v0.5.13
   [94e857df] SIMDTypes v0.1.0
   [476501e8] SLEEFPirates v0.6.42
-  [0bca4576] SciMLBase v2.35.0
+  [0bca4576] SciMLBase v2.36.0
   [c0aeaf25] SciMLOperators v0.3.8
   [1ed8b502] SciMLSensitivity v7.56.2
   [53ae85a6] SciMLStructures v1.1.0
@@ -213,7 +213,7 @@
   [892a3eda] StringManipulation v0.3.4
   [09ab397b] StructArrays v0.6.18
   [53d494c1] StructIO v0.3.0
-  [2efcf032] SymbolicIndexingInterface v0.3.16
+  [2efcf032] SymbolicIndexingInterface v0.3.20
   [3783bdb8] TableTraits v1.0.1
   [bd369af6] Tables v1.11.1
   [8290d209] ThreadingUtilities v0.5.2
@@ -227,7 +227,7 @@
   [3a884ed6] UnPack v1.0.2
   [013be700] UnsafeAtomics v0.2.1
   [d80eeb9a] UnsafeAtomicsLLVM v0.1.3
-  [3d5dd08c] VectorizationBase v0.21.66
+  [3d5dd08c] VectorizationBase v0.21.67
   [19fa3120] VertexSafeGraphs v0.2.0
   [e88e6eb3] Zygote v0.6.69
   [700de1a5] ZygoteRules v0.2.5
@@ -236,7 +236,7 @@
   [76a88914] CUDA_Runtime_jll v0.12.1+0
   [62b44479] CUDNN_jll v9.0.0+1
 ⌅ [7cc45869] Enzyme_jll v0.0.102+0
-  [2e619515] Expat_jll v2.5.0+0
+  [2e619515] Expat_jll v2.6.2+0
   [f8c6e375] Git_jll v2.44.0+2
   [1d5cc7b8] IntelOpenMP_jll v2024.1.0+0
   [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
@@ -282,7 +282,7 @@
   [8dfed614] Test
   [cf7118a7] UUIDs
   [4ec0a83e] Unicode
-  [e66e0078] CompilerSupportLibraries_jll v1.1.0+0
+  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
   [deac9b47] LibCURL_jll v8.4.0+0
   [e37daf67] LibGit2_jll v1.6.4+0
   [29816b5a] LibSSH2_jll v1.11.0+1
@@ -296,4 +296,4 @@
   [8e850b90] libblastrampoline_jll v5.8.0+1
   [8e850ede] nghttp2_jll v1.52.0+1
   [3f19e933] p7zip_jll v17.4.0+2
-Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.

+Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.

diff --git a/dev/problems/index.html b/dev/problems/index.html index b11b48e..0b32dfe 100644 --- a/dev/problems/index.html +++ b/dev/problems/index.html @@ -31,4 +31,4 @@

Defines a Parabolic Partial Differential Equation of the form:

\[\begin{aligned} \frac{du}{dt} &= \tfrac{1}{2} \text{Tr}(\sigma \sigma^T) \Delta u(x, t) + \mu \nabla u(x, t) \\ &\quad + f(x, u(x, t), ( \nabla_x u )(x, t), p, t) -\end{aligned}\]

Arguments

Optional Arguments

source
Note

While choosing to define a PDE using PIDEProblem, note that the function being integrated f is a function of f(x, y, v_x, v_y, ∇v_x, ∇v_y) out of which y is the integrating variable and x is constant throughout the integration. If a PDE has no integral and the non linear term f is just evaluated as f(x, v_x, ∇v_x) then we suggest using ParabolicPDEProblem

+\end{aligned}\]

Arguments

Optional Arguments

source
Note

While choosing to define a PDE using PIDEProblem, note that the function being integrated f is a function of f(x, y, v_x, v_y, ∇v_x, ∇v_y) out of which y is the integrating variable and x is constant throughout the integration. If a PDE has no integral and the non linear term f is just evaluated as f(x, v_x, ∇v_x) then we suggest using ParabolicPDEProblem

diff --git a/dev/tutorials/deepbsde/index.html b/dev/tutorials/deepbsde/index.html index a05d343..fd728bb 100644 --- a/dev/tutorials/deepbsde/index.html +++ b/dev/tutorials/deepbsde/index.html @@ -67,4 +67,4 @@ Dense(hls,hls,relu), Dense(hls,d)) pdealg = NNPDENS(u0, σᵀ∇u, opt=opt)

And now we solve the PDE. Here, we say we want to solve the underlying neural SDE using the Euler-Maruyama SDE solver with our chosen dt=0.2, do at most 150 iterations of the optimizer, 100 SDE solves per loss evaluation (for averaging), and stop if the loss ever goes below 1f-6.

ans = solve(prob, pdealg, verbose=true, maxiters=150, trajectories=100,
-                            alg=EM(), dt=0.2, pabstol = 1f-6)

References

  1. Shinde, A. S., and K. C. Takale. "Study of Black-Scholes model and its applications." Procedia Engineering 38 (2012): 270-279.
+ alg=EM(), dt=0.2, pabstol = 1f-6)

References

  1. Shinde, A. S., and K. C. Takale. "Study of Black-Scholes model and its applications." Procedia Engineering 38 (2012): 270-279.
diff --git a/dev/tutorials/deepsplitting/index.html b/dev/tutorials/deepsplitting/index.html index a621251..5e2eddb 100644 --- a/dev/tutorials/deepsplitting/index.html +++ b/dev/tutorials/deepsplitting/index.html @@ -41,4 +41,4 @@ abstol = 2e-3, maxiters = 1000, batch_size = 1000, - use_cuda=true) + use_cuda=true) diff --git a/dev/tutorials/mlp/index.html b/dev/tutorials/mlp/index.html index adb02ec..452ca86 100644 --- a/dev/tutorials/mlp/index.html +++ b/dev/tutorials/mlp/index.html @@ -31,4 +31,4 @@ ## Definition of the algorithm alg = MLP(mc_sample = mc_sample ) -sol = solve(prob, alg, multithreading=true) +sol = solve(prob, alg, multithreading=true) diff --git a/dev/tutorials/nnkolmogorov/index.html b/dev/tutorials/nnkolmogorov/index.html index bfce717..56d8dfa 100644 --- a/dev/tutorials/nnkolmogorov/index.html +++ b/dev/tutorials/nnkolmogorov/index.html @@ -25,4 +25,4 @@ alg = NNKolmogorov(m, opt) m = Chain(Dense(d, 16, elu), Dense(16, 32, elu), Dense(32, 16, elu), Dense(16, 1)) sol = solve(prob, alg, sdealg, verbose = true, dt = 0.01, - dx = 0.0001, trajectories = 1000, abstol = 1e-6, maxiters = 300) + dx = 0.0001, trajectories = 1000, abstol = 1e-6, maxiters = 300) diff --git a/dev/tutorials/nnparamkolmogorov/index.html b/dev/tutorials/nnparamkolmogorov/index.html index 83f15e3..11e5e93 100644 --- a/dev/tutorials/nnparamkolmogorov/index.html +++ b/dev/tutorials/nnparamkolmogorov/index.html @@ -43,4 +43,4 @@ p_sigma_test = rand(p_domain.p_sigma[1]:dps.p_sigma:p_domain.p_sigma[2], 1, 1) t_test = rand(tspan[1]:dt:tspan[2], 1, 1) p_mu_test = nothing -p_phi_test = nothing
sol.ufuns(x_test, t_test, p_sigma_test, p_mu_test, p_phi_test)
+p_phi_test = nothing
sol.ufuns(x_test, t_test, p_sigma_test, p_mu_test, p_phi_test)
diff --git a/dev/tutorials/nnstopping/index.html b/dev/tutorials/nnstopping/index.html index 299fa56..34bd93b 100644 --- a/dev/tutorials/nnstopping/index.html +++ b/dev/tutorials/nnstopping/index.html @@ -21,4 +21,4 @@ for i in 1:N]
Note

The number of models should be equal to the time discritization.

And finally we define our optimizer and algorithm, and call solve:

opt = Flux.Optimisers.Adam(0.01)
 alg = NNStopping(models, opt)
 
-sol = solve(prob, alg, SRIW1(); dt = dt, trajectories = 1000, maxiters = 1000, verbose = true)
+sol = solve(prob, alg, SRIW1(); dt = dt, trajectories = 1000, maxiters = 1000, verbose = true)