Stochastic Optimization under high-dimensional Uncertainty in Python—SOUPy, implements scalable algorithms for the optimization of large-scale complex systems governed by partial differential equations (PDEs) under high-dimensional uncertainty. The library features various risk measures (such as mean, variance, and superquantile/condition-value-at-risk), probability/chance constraints, and optimization/state constraints. SOUPy enables efficient PDE-constrained optimization under uncertainty through parallel computation of the risk measures and their derivatives (gradients and Hessians). The library also provides built-in parallel implementations of optimization algorithms (e.g. BFGS, Inexact Newton CG), as well as an interface to the scipy.optimize module in SciPy. Besides the benchmark/tutorial examples in the examples folder, SOUPy has been used to solve large-scale and high-dimensional stochastic optimization problems including optimal control of turbulence flow, optimal design of acoustic metamaterials and self-assembly nanomaterials, and optimal management of groundwater extraction, etc.
SOUPy is built on the open-source hIPPYlib library, which provides adjoint-based methods for deterministic and Bayesian inverse problems governed by PDEs, and makes use of FEniCS for the high-level formulation, discretization, and solution of PDEs.
SOUPy is in active development to incorporate advanced approximation algorithms and capabilities, including:
- Taylor expansion-based approximations for risk measure evaluation
- High-dimensional quadrature methods such as sparse grids and quasi Monte Carlo
- Decomposition of high-dimensional uncertain parameter spaces by mixture models
- Multi-fidelity methods and control variates
- Interfaces with Bayesian inverse problems
See the SOUPy documentation and our JOSS paper for more information.
Please cite SOUPy as
@article{Luo2024,
doi = {10.21105/joss.06101},
url = {https://doi.org/10.21105/joss.06101},
year = {2024},
publisher = {The Open Journal},
volume = {9},
number = {99},
pages = {6101},
author = {Dingcheng Luo and Peng Chen and Thomas O'Leary-Roseberry and Umberto Villa and Omar Ghattas},
title = {{SOUPy}: Stochastic PDE-constrained optimization under high-dimensional uncertainty in Python},
journal = {Journal of Open Source Software}
}
This project is partially supported by NSF grants #2012453 and #2245674.