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BayesiaNODE_SGHMC_spiral.jl
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using Distributed
using DiffEqFlux, OrdinaryDiffEq, Flux, Optim, Turing, Serialization, Plots
using JLD
u0 = [2.0; 0.0]
datasize = 60
tspan = (0.0, 1.2)
tsteps = range(tspan[1], tspan[2], length = datasize)
function spiral(du, u, p, t)
true_A = [-0.1 2.0; -2.0 -0.1]
du .= ((u.^3)'true_A)'
end
trueodeprob = ODEProblem(spiral, u0, tspan);
ode_data = Array(solve(trueodeprob, Tsit5(), saveat = tsteps));
y_train = ode_data[:, 1:50];
dudt2 = FastChain(FastDense(2, 50, tanh),
FastDense(50, 2))
prob_node = NeuralODE(dudt2, tspan, Tsit5(), saveat = tsteps); #neural ode
train_prob = NeuralODE(dudt2, (0., 1.0), Tsit5(), saveat = tsteps[1:50]);
function predict_node(p) # predict with given params
Array(train_prob(u0, p))
end
function loss(p) # loss function to minimize
pred = predict_node(p)
return Float64(sum(abs2, y_train .- pred))
end
## -----------------------------
####### Perform inference
### Fit neural ode to the data
@everywhere @model function fit_node(data)
σ ~ InverseGamma(2, 3)
p ~ MvNormal(pmin_spiral, 0.1)
# Calculate predictions for the inputs given the params.
predicted = train_prob(u0, p)
# observe each prediction.
for i = 1:size(predicted,2)
data[:,i] ~ MvNormal(predicted[:,i], σ)
end
end
@everywhere model = fit_node(y_train); # fit model to average simulated data
function perform_inference(lr, alpha, samplesize, pmin, num_chains)
alg = SGHMC(learning_rate=lr, momentum_decay=alpha)
chain = sample(model, alg, MCMCThreads(), samplesize, num_chains, progress=true);
return chain
end
function map_loss(chain)
chain_array = Array(chain)
k = size(chain_array,1)
losses = loss.([chain_array[i,:] for i in 1:k])
return losses
end
callback = function (p, l, param; doplot = true)
# plot current prediction against data
display(l)
plt = scatter(ode_data[1,:], ode_data[2,:], label = "data")
sol = prob_node(u0, param);
scatter!(plt, sol[1,:], sol[2,:], label = "prediction")
if doplot
display(plot(plt))
end
return false
end
# init at map point
using JLD
pinit = initial_params(dudt2);
opt = DiffEqFlux.sciml_train(loss, train_prob.p, ADAM(0.05), maxiters = 1500)
pmin = opt.minimizer;
save("pmin_spiral.jld", "pmin_spiral", pmin)
using JLD
pmin = load("pmin_spiral.jld")
pmin_spiral = pmin["pmin_spiral"]
sol = prob_node(u0, pmin_spiral);
plot()
display(scatter!(sol[1,:], sol[2,:]))
display(scatter!(ode_data[1,:], ode_data[2,:]))
function plot_chain(chain, losses)
pl = plot()
chain_array = Array(chain)
len = size(chain_array,1)
training_end = 1.0
tei = 50 #training_end_idx
scatter!(tsteps, ode_data[1,:], color = :red, label = "Data: Var1", title = "Spiral Neural ODE")
scatter!(tsteps, ode_data[2,:], color = :blue, label = "Data: Var2")
plot!([training_end-0.0001,training_end+0.0001],[-2.2,1.3],lw=3,color=:green,label="Training Data End", linestyle = :dash)
for k in 1:300
resol = prob_node(u0, chain_array[rand(100:len), :])
plot!(tsteps[1:tei], resol[1,:][1:tei], alpha=0.04, color = :red, label = "")
plot!(tsteps[1:tei], resol[2,:][1:tei], alpha=0.04, color = :blue, label = "")
plot!(tsteps[tei:end], resol[1,:][tei:end], alpha=0.04, color = :purple, label = "")
plot!(tsteps[tei:end], resol[2,:][tei:end], alpha=0.04, color = :purple, label = "")
end
idx = findmin(losses)[2]
prediction = prob_node(u0, chain_array[idx, :])
plot!(tsteps, prediction[1,:], color=:black, w=2, label = "")
plot!(tsteps, prediction[2,:], color=:black, w=2, label = "Training: Best fit prediction", ylims = (-2.5, 3.5))
plot!(tsteps[tei:end], prediction[1,:][tei:end], color = :purple, w = 2, label = "")
plot!(tsteps[tei:end], prediction[2,:][tei:end], color = :purple, w = 2, label = "Forecasting: Best fit prediction", ylims = (-2.5, 3.5))
display(plot!([training_end-0.0001,training_end+0.0001],[-1,5],lw=3,color=:green,label="Training Data End", linestyle = :dash))
################## COUNTOUR PLOTS ###################################
pl2 = scatter(ode_data[1,:], ode_data[2,:], color = :red, label = "Data", xlabel = "Var1", ylabel = "Var2", title = "Spiral Neural ODE")
for k in 1:300
resol = prob_node(u0, chain_array[rand(50:len), :])
plot!(resol[1,:][1:tei],resol[2,:][1:tei], alpha=0.04, color = :red, label = "")
plot!(resol[1,:][tei:end],resol[2,:][tei:end], alpha=0.1, color = :purple, label = "")
end
plot!(prediction[1,:], prediction[2,:], color = :black, w = 2, label = "Training: Best fit prediction", ylims = (-2.5, 3.5))
display(plot!(prediction[1,:][tei:end], prediction[2,:][tei:end], color = :purple, w = 2, label = "Forecasting: Best fit prediction", ylims = (-2.5, 3.5)))
return pl, pl2;
end
## ---------------------------------------------------
#
samples = 750
lr = 1.0e-6; md = 0.15;
num_chains = 6;
chain = perform_inference(lr, md, samples, pmin, num_chains);
for i in 1:num_chains
losses = map_loss(chain[:,:,i])
pl = plot(1:samples, losses); display(pl)
savefig(pl, string("spiral_", lr, "_", md, "_", samples, "_", "chain_", i+4, "_losses", ".png"))
pl_ch, pl2 = plot_chain(chain[:,:,i], losses)
savefig(pl_ch, string("spiral_", lr, "_", md, "_", samples, "_", "chain_", i+4, "_predictions", ".png"))
savefig(pl2, string("spiral_", lr, "_", md, "_", samples, "_", "chain_", i+4, "_contour", ".png"))
end