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 for more information.

Please consider to cite the following papers for using SOUPy

@article{chen2019taylor,
  title={Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty},
  author={Chen, Peng and Villa, Umberto and Ghattas, Omar},
  journal={Journal of Computational Physics},
  volume={385},
  pages={163--186},
  year={2019},
  publisher={Elsevier}
}

@article{luo2023efficient,
  title={Efficient PDE-Constrained optimization under high-dimensional uncertainty using derivative-informed neural operators},
  author={Luo, Dingcheng and O'Leary-Roseberry, Thomas and Chen, Peng and Ghattas, Omar},
  journal={arXiv preprint arXiv:2305.20053},
  year={2023}
}

This project is partially supported by NSF grants #2012453 and #2245674.