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https://joss.theoj.org/papers/10.21105/joss.06101.pdf + + + + + + Taylor approximation and variance reduction +for PDE-constrained optimal control under uncertainty + Chen + Journal of Computational +Physics + 385 + 10.1016/j.jcp.2019.01.047 + 2019 + Chen, P., Villa, U., & Ghattas, +O. (2019). Taylor approximation and variance reduction for +PDE-constrained optimal control under uncertainty. Journal of +Computational Physics, 385, 163–186. +https://doi.org/10.1016/j.jcp.2019.01.047 + + + Optimal design of acoustic metamaterial +cloaks under uncertainty + Chen + Journal of Computational +Physics + 431 + 10.1016/j.jcp.2021.110114 + 2021 + Chen, P., Haberman, M., & +Ghattas, O. (2021). Optimal design of acoustic metamaterial cloaks under +uncertainty. Journal of Computational Physics, 431, 110114. +https://doi.org/10.1016/j.jcp.2021.110114 + + + HIPPYlib: An extensible software framework +for large-scale inverse problems governed by PDEs: Part I: Deterministic +inversion and linearized Bayesian inference + Villa + ACM Transactions on Mathematical +Software + 2 + 47 + 10.1145/3428447 + 0098-3500 + 2021 + Villa, U., Petra, N., & Ghattas, +O. (2021). HIPPYlib: An extensible software framework for large-scale +inverse problems governed by PDEs: Part I: Deterministic inversion and +linearized Bayesian inference. ACM Transactions on Mathematical +Software, 47(2). https://doi.org/10.1145/3428447 + + + hIPPYlib: an Extensible Software Framework +for Large-scale Deterministic and Bayesian Inverse +Problems + Villa + Journal of Open Source +Software + 30 + 3 + 10.21105/joss.00940 + 2018 + Villa, U., Petra, N., & Ghattas, +O. (2018). hIPPYlib: an Extensible Software Framework for Large-scale +Deterministic and Bayesian Inverse Problems. Journal of Open Source +Software, 3(30). +https://doi.org/10.21105/joss.00940 + + + Efficient PDE-constrained optimization under +high-dimensional uncertainty using derivative-informed neural +operators + Luo + 10.48550/arXiv.2305.20053 + 2023 + Luo, D., O’Leary-Roseberry, T., Chen, +P., & Ghattas, O. (2023). Efficient PDE-constrained optimization +under high-dimensional uncertainty using derivative-informed neural +operators. +https://doi.org/10.48550/arXiv.2305.20053 + + + Automated solution of differential equations +by the finite element method + 84 + 10.1007/978-3-642-23099-8 + 2012 + Logg, A., Mardal, K.-A., & Wells, +G. N. (Eds.). (2012). Automated solution of differential equations by +the finite element method (Vol. 84). Springer. +https://doi.org/10.1007/978-3-642-23099-8 + + + SciPy 1.0: Fundamental algorithms for +scientific computing in Python + Virtanen + Nature Methods + 17 + 10.1038/s41592-019-0686-2 + 2020 + Virtanen, P., Gommers, R., Oliphant, +T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, +P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, +J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., +Larson, E., … SciPy 1.0 Contributors. (2020). SciPy 1.0: Fundamental +algorithms for scientific computing in Python. Nature Methods, 17, +261–272. +https://doi.org/10.1038/s41592-019-0686-2 + + + On the limited memory BFGS methods for large +scale optimization + Liu + Mathematical Programming + 45 + 10.1007/BF01589116 + 1989 + Liu, D. C., & Nocedal, J. (1989). +On the limited memory BFGS methods for large scale optimization. +Mathematical Programming, 45, 503–528. +https://doi.org/10.1007/BF01589116 + + + Local and superlinear convergence for +truncated iterated projections methods + Steihaug + Mathematical Programming + 27 + 10.1007/BF02591944 + 1983 + Steihaug, T. (1983). Local and +superlinear convergence for truncated iterated projections methods. +Mathematical Programming, 27, 176–190. +https://doi.org/10.1007/BF02591944 + + + Choosing the forcing terms in an inexact +Newton method + Eisenstat + SIAM Journal on Scientific +Computing + 1 + 17 + 10.1137/0917003 + 1996 + Eisenstat, S. C., & Walker, H. F. +(1996). Choosing the forcing terms in an inexact Newton method. SIAM +Journal on Scientific Computing, 17(1), 16–32. +https://doi.org/10.1137/0917003 + + + Taylor approximation for chance constrained +optimization problems governed by partial differential equations with +high-dimensional random parameters + Chen + SIAM/ASA Journal on Uncertainty +Quantification + 4 + 9 + 10.1137/20M1381381 + 2021 + Chen, P., & Ghattas, O. (2021). +Taylor approximation for chance constrained optimization problems +governed by partial differential equations with high-dimensional random +parameters. SIAM/ASA Journal on Uncertainty Quantification, 9(4), +1381–1410. https://doi.org/10.1137/20M1381381 + + + Dolfin-adjoint 2018.1: Automated adjoints for +FEniCS and firedrake + Mitusch + Journal of Open Source +Software + 38 + 4 + 10.21105/joss.01292 + 2019 + Mitusch, S. K., Funke, S. W., & +Dokken, J. S. (2019). Dolfin-adjoint 2018.1: Automated adjoints for +FEniCS and firedrake. 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Optimal design of photonic nanojets under +uncertainty. +https://doi.org/10.48550/arXiv.2209.02454 + + + Optimization of PDEs with uncertain +inputs + Kouri + Frontiers in PDE-constrained +optimization + 10.1007/978-1-4939-8636-1_2 + 978-1-4939-8636-1 + 2018 + Kouri, D. P., & Shapiro, A. +(2018). Optimization of PDEs with uncertain inputs. In H. Antil, D. P. +Kouri, M.-D. Lacasse, & D. Ridzal (Eds.), Frontiers in +PDE-constrained optimization (pp. 41–81). Springer New York. +https://doi.org/10.1007/978-1-4939-8636-1_2 + + + Rapid optimization library + Kouri + 2017 + Kouri, D., Ridzal, D., & Winckel, +G. von. (2017). Rapid optimization library. Sandia National +Laboratories. +https://trilinos.github.io/pdfs/ROL.pdf + + + Optimization of conditional +value-at-risk + Rockafellar + The Journal of Risk + 3 + 2 + 10.21314/jor.2000.038 + 2000 + Rockafellar, R. T., & Uryasev, S. +(2000). Optimization of conditional value-at-risk. The Journal of Risk, +2(3), 21–41. +https://doi.org/10.21314/jor.2000.038 + + + + + + From e266da7d277de5d6edebeeb4a5c1f4229812881b Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Sun, 28 Jul 2024 14:23:42 +0100 Subject: [PATCH 3/3] Creating 10.21105.joss.06101.jats --- .../paper.jats/10.21105.joss.06101.jats | 565 ++++++++++++++++++ 1 file changed, 565 insertions(+) create mode 100644 joss.06101/paper.jats/10.21105.joss.06101.jats diff --git a/joss.06101/paper.jats/10.21105.joss.06101.jats b/joss.06101/paper.jats/10.21105.joss.06101.jats new file mode 100644 index 0000000000..20822a2dbe --- /dev/null +++ b/joss.06101/paper.jats/10.21105.joss.06101.jats @@ -0,0 +1,565 @@ + + +

+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6101 +10.21105/joss.06101 + +SOUPy: Stochastic PDE-constrained optimization under +high-dimensional uncertainty in Python + + + + +Luo +Dingcheng + + + + + +Chen +Peng + + + + + +O’Leary-Roseberry +Thomas + + + + + +Villa +Umberto + + + + + +Ghattas +Omar + + + + + + +Oden Institute for Computational Engineering and Sciences, +The University of Texas at Austin, USA + + + + +School of Computational Science and Engineering, Georgia +Institute of Technology, USA + + + + +Walker Department of Mechanical Engineering, The University +of Texas at Austin, USA + + + + +22 +9 +2023 + +9 +99 +6101 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Python +Uncertainty quantification +PDE-constrained optimization +Optimization under uncertainty +Adjoint method + + + + + + Summary +

Computational models governed by partial differential equations + (PDEs) are frequently used by engineers to optimize the performance of + various physical systems through decisions relating to their + configuration (optimal design) and operation (optimal control). + However, the ability to make optimal choices is often hindered by + uncertainty, such as uncertainty in model parameters (e.g., material + properties) and operating conditions (e.g., forces on a structure). + The need to account for these uncertainties in order to arrive at + robust and risk-informed decisions thus gives rise to problems of + optimization under uncertainty (OUU) + (D. + P. Kouri & Shapiro, 2018).

+

SOUPy is a Python library for solving PDE-constrained optimization + problems with uncertain parameters, where we use the term + parameters broadly to refer to sources and + initial/boundary conditions in addition to PDE coefficients. The + optimization problem is defined by a risk measure over a given + quantity of interest (QoI), which is present as either an optimization + objective or constraint (as in chance-constrained optimization). + Specific attention is given to the case where the uncertain parameters + are formally infinite dimensional (e.g., Gaussian random fields). The + software allows users to supply the underlying PDE model, quantity of + interest, and penalty terms, and provides implementations for commonly + used risk measures, including expectation, variance, and + superquantile/conditional value-at-risk (CVaR) + (Rockafellar + & Uryasev, 2000), as well as derivative-based optimizers. + SOUPy leverages FEniCS + (Logg + et al., 2012) for the formulation, discretization, and solution + of PDEs, and the framework of hIPPYlib + (U. + Villa et al., 2018; + Umberto + Villa et al., 2021) for sampling from random fields and + automating adjoint-based derivative computation, while also providing + interfaces to existing optimization algorithms in SciPy.

+
+ + Statement of need +

Problems of PDE-constrained optimization under uncertainty arise + due to the ubiquity of uncertainty in natural and engineered systems. + In deterministic PDE-constrained optimization, the goal is typically + to optimize a quantity of interest (QoI) that is a function of the + system’s state and quantifies its performance, where the optimization + and state variables are related through the underlying PDE model. + Compared to this deterministic counterpart, PDE-constrained OUU + involves an added layer of complexity, since the QoI becomes a random + variable due to its dependence on the uncertain model parameters. In + OUU, the cost functional and/or constraints are instead given in terms + of risk measures, which are statistical quantities summarizing the + QoI’s distribution. A canonical example of such a risk measure is the + expected value of the QoI, though other measures that account for the + tail behavior of the distribution such as the variance, or + superquantile/CVaR are common choices. Computation of risk measures + typically requires sampling or quadrature methods to approximate the + integral over the distribution of the uncertain parameter. This + results in a complex optimization problem in which each evaluation of + the optimization objective requires numerous solutions of the + underlying PDE.

+

Several open-source software packages such as dolfin-adjoint + (Mitusch + et al., 2019) and hIPPYlib provide the capabilities for solving + PDE-constrained optimization problems with generic PDEs using + derivatives computed by adjoint sensitivity methods. However, these + packages largely focus on the deterministic setting. On the other + hand, the Rapid Optimization Library (ROL) + (D. + Kouri et al., 2017), released as a part of Trilinos + (Trilinos + Project Team, 2024), provides advanced algorithms for both + deterministic and stochastic (risk measure) optimization, where + support for PDE-constrained OUU is enabled by its interfaces with + user-supplied state and adjoint PDE solvers.

+

SOUPy aims to provide a unified platform to formulate and solve + PDE-constrained OUU problems using efficient derivative-based + optimization methods. Users can supply the definitions for the PDE + constraint, QoI, and additional penalty terms that account for the + cost of design/control, and are then given the option to choose from a + suite of risk measures to optimize. To this end, SOUPy makes use of + FEniCS, an open source finite element library, to create and solve the + underlying PDEs. The unified form language (UFL) + (Alnæs + et al., 2014) used by FEniCS allows users to conveniently + define the PDE, QoI, and penalty terms in their variational forms. + SOUPy is also integrated with hIPPYlib, an open source library for + large-scale inverse problems, adopting its framework for automating + adjoint-based derivative computation by leveraging the symbolic + differentiation capabilities of UFL and algorithms for efficient + sampling of random fields. As a core functionality, SOUPy implements + sample-based evaluation of risk measures as well as their gradients + and Hessians, where parallel-in-sample computation is supported + through MPI. The resulting cost functionals can then be minimized + using SOUPy’s implementations of large-scale optimization algorithms, + such as L-BFGS + (Liu + & Nocedal, 1989) and Inexact Newton-CG + (Eisenstat + & Walker, 1996; + Steihaug, + 1983), or through algorithms available in SciPy + (Virtanen + et al., 2020) using the provided interface.

+

Thus, SOUPy allows researchers to rapidly prototype formulations + for PDE-constrained OUU problems. Additionally, SOUPy aims to + facilitate the development and testing of novel algorithms. For + example, SOUPy has been used in the development of Taylor + approximation-based methods for the risk-averse optimization of + turbulent flows + (Chen + et al., 2019), metamaterial design + (Chen + et al., 2021), and photonic nanojets + (Alghamdi + et al., 2022), as well as groundwater extraction + (Chen + & Ghattas, 2021) subject to chance constraints. It has also + been used to obtain baselines for the development of machine learning + approaches for PDE-constrained OUU + (Luo + et al., 2023).

+
+ + Acknowledgements +

This project is partially supported by NSF grants 2012453 and + 2245674 and DOE grants DE-SC0019303 and DE-SC0023171

+
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