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.


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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.
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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.
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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.
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Zammit-Mangion, Andrew, and Jonathan Rougier. 2019. Multi-Scale Process Modelling and Distributed Computation for Spatial Data,” July.

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