Inverse problems for complex models

a.k.a. Bayesian calibration, model uncertainty



Inverse problems where the model is more or less a black box.

References

Brehmer, Johann, Gilles Louppe, Juan Pavez, and Kyle Cranmer. 2020. “Mining Gold from Implicit Models to Improve Likelihood-Free Inference.” Proceedings of the National Academy of Sciences 117 (10): 5242–49. https://doi.org/10.1073/pnas.1915980117.
Cranmer, Kyle, Johann Brehmer, and Gilles Louppe. 2020. “The Frontier of Simulation-Based Inference.” Proceedings of the National Academy of Sciences, May. https://doi.org/10.1073/pnas.1912789117.
Grigorievskiy, Alexander, Neil Lawrence, and Simo Särkkä. 2017. “Parallelizable Sparse Inverse Formulation Gaussian Processes (SpInGP).” In arXiv:1610.08035 [stat]. http://arxiv.org/abs/1610.08035.
Plumlee, Matthew. 2017. “Bayesian Calibration of Inexact Computer Models.” Journal of the American Statistical Association 112 (519): 1274–85. https://doi.org/10.1080/01621459.2016.1211016.
Tait, Daniel J., and Theodoros Damoulas. 2020. “Variational Autoencoding of PDE Inverse Problems.” arXiv:2006.15641 [cs, Stat], June. http://arxiv.org/abs/2006.15641.
Welter, David E., Jeremy T. White, Randall J. Hunt, and John E. Doherty. 2015. “Approaches in Highly Parameterized Inversion—PEST++ Version 3, a Parameter ESTimation and Uncertainty Analysis Software Suite Optimized for Large Environmental Models.” USGS Numbered Series 7-C12. Techniques and Methods. Reston, VA: U.S. Geological Survey. https://doi.org/10.3133/tm7C12.
White, Jeremy T., Michael N. Fienen, and John E. Doherty. 2016a. pyEMU: A Python Framework for Environmental Model Uncertainty Analysis Version .01. U.S. Geological Survey. https://doi.org/10.5066/F75D8Q01.
———. 2016b. “A Python Framework for Environmental Model Uncertainty Analysis.” Environmental Modelling & Software 85 (November): 217–28. https://doi.org/10.1016/j.envsoft.2016.08.017.
Zammit-Mangion, Andrew, Michael Bertolacci, Jenny Fisher, Ann Stavert, Matthew L. Rigby, Yi Cao, and Noel Cressie. 2021. “WOMBAT v1.0: A fully Bayesian global flux-inversion framework.” Geoscientific Model Development Discussions, July, 1–51. https://doi.org/10.5194/gmd-2021-181.
Zhang, Dongkun, Lu Lu, Ling Guo, and George Em Karniadakis. 2019. “Quantifying Total Uncertainty in Physics-Informed Neural Networks for Solving Forward and Inverse Stochastic Problems.” Journal of Computational Physics 397 (November): 108850. https://doi.org/10.1016/j.jcp.2019.07.048.

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