README.md

Derivative-informed neural operators for optimization under uncertainty

The this repository contains code for the numerical examples in the paper "Efficient PDE-constrained optimization under high dimensional uncertainty using derivative-informed neural operators". Specifically, it includes the data generation, training, and OUU codes for the semilinear elliptic PDE problem and the 2D Navier--Stokes flow control problem. Data generation code for 3D example is not included but can be made available upon request (email the author at dc.luo@utexas.edu).

Installation

The code uses FEniCS for finite element computations and tensorflow for machine learning. This along with additional requirements are listed in environment.yml, and can be installed via conda using

conda env create -f environment.yml

Additionally, the code makes use of hIPPYLib, hIPPYflow and SOUPy from the hIPPYLib organization to handle the data generation. SOUPy is also used for optimization under uncertainty. We suggest cloning these repositories

git clone https://github.com/hippylib/hippylib.git
git clone https://github.com/hippylib/hippyflow.git
git clone https://github.com/hippylib/soupy.git

and setting the path to their base directories

conda activate mr_dino
conda env config vars set HIPPYLIB_PATH=path/to/hippylib
conda env config vars set HIPPYFLOW_PATH=path/to/hippyflow
conda env config vars set SOUPY_PATH=path/to/soupy
conda deactivate