Multi fidelity models

Data-driven coarse graining. Also multi-scale models.



At the collision of coarse graining and sampling theory, we have multi-fidelity modeling, which is an attempt to do tries to harness the efficiency of lower-precision and higher-precision models together adaptively in some sense. This name is a Machine Learning name; I presume that this concept has been invented many times under other names, which I will add when I learn them.

References

Cranmer, Kyle, Johann Brehmer, and Gilles Louppe. 2020. The Frontier of Simulation-Based Inference.” Proceedings of the National Academy of Sciences, May.
Cutajar, Kurt, Mark Pullin, Andreas Damianou, Neil Lawrence, and Javier González. 2019. Deep Gaussian Processes for Multi-Fidelity Modeling.” arXiv:1903.07320 [Cs, Stat], March.
Forrester, Alexander I. J., and Andy J. Keane. 2009. Recent Advances in Surrogate-Based Optimization.” Progress in Aerospace Sciences 45 (1–3): 50–79.
Kennedy, M. C., and A. O’Hagan. 2000. Predicting the Output from a Complex Computer Code When Fast Approximations Are Available.” Biometrika 87 (1): 1–13.
Kennedy, Marc C., and Anthony O’Hagan. 2001. Bayesian Calibration of Computer Models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (3): 425–64.
Kochkov, Dmitrii, Jamie A. Smith, Ayya Alieva, Qing Wang, Michael P. Brenner, and Stephan Hoyer. 2021. Machine Learning–Accelerated Computational Fluid Dynamics.” Proceedings of the National Academy of Sciences 118 (21).
Meng, Xuhui, Hessam Babaee, and George Em Karniadakis. 2021. Multi-Fidelity Bayesian Neural Networks: Algorithms and Applications.” Journal of Computational Physics 438 (August): 110361.
Oladyshkin, S., and W. Nowak. 2012. Data-Driven Uncertainty Quantification Using the Arbitrary Polynomial Chaos Expansion.” Reliability Engineering & System Safety 106 (October): 179–90.
Perdikaris, Paris, Daniele Venturi, and George Em Karniadakis. 2016. Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data Sets.” SIAM Journal on Scientific Computing 38 (4): B521–38.
Perdikaris, P., M. Raissi, A. Damianou, N. D. Lawrence, and G. E. Karniadakis. 2017. Nonlinear Information Fusion Algorithms for Data-Efficient Multi-Fidelity Modelling.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2198): 20160751.
Perdikaris, P., D. Venturi, J. O. Royset, and G. E. Karniadakis. 2015. Multi-Fidelity Modelling via Recursive Co-Kriging and Gaussian–Markov Random Fields.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2179): 20150018.
Queipo, Nestor V., Raphael T. Haftka, Wei Shyy, Tushar Goel, Rajkumar Vaidyanathan, and P. Kevin Tucker. 2005. Surrogate-Based Analysis and Optimization.” Progress in Aerospace Sciences 41 (1): 1–28.
Raissi, Maziar, and George Karniadakis. 2016. Deep Multi-Fidelity Gaussian Processes.” arXiv:1604.07484 [Cs, Stat], April.
Razavi, Saman, Bryan A. Tolson, and Donald H. Burn. 2012. Review of Surrogate Modeling in Water Resources.” Water Resources Research 48 (7).
Sarkar, Soumalya, and Michael Joly. 2019. Multi-FIdelity Learning with Heterogeneous Domains.” In NeurIPS, 5.
Tu, Jonathan H., Clarence W. Rowley, Dirk M. Luchtenburg, Steven L. Brunton, and J. Nathan Kutz. 2014. On Dynamic Mode Decomposition: Theory and Applications.” Journal of Computational Dynamics 1 (2): 391.
Watson, James, and Chris Holmes. 2016. Approximate Models and Robust Decisions.” Statistical Science 31 (4): 465–89.
Zammit-Mangion, Andrew, and Jonathan Rougier. 2019. Multi-Scale Process Modelling and Distributed Computation for Spatial Data,” July.

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