Multi fidelity models

Data-driven multi-scale sampling



The pun here is too delicious for me not to use this 1885 cartoon; yes I am aware that marital dynamics are more nuanced amongst adherents of the LDS than the gentleman depicted seems to believe.

At the collision of coarse graining and sampling theory and variational inference, we have multi-fidelity modeling, which is an attempts to harness the efficiency of lower-precision and higher-precision models together. 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. Possibly one of those names is learnable coarse graining

References

Altmann, Robert, Patrick Henning, and Daniel Peterseim. 2021. Numerical Homogenization Beyond Scale Separation.” Acta Numerica 30 (May): 1–86.
Chan, Henry, Mathew J. Cherukara, Badri Narayanan, Troy D. Loeffler, Chris Benmore, Stephen K. Gray, and Subramanian K. R. S. Sankaranarayanan. 2019. Machine Learning Coarse Grained Models for Water.” Nature Communications 10 (1): 379.
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.
Fu, Xiang, Tian Xie, Nathan J. Rebello, Bradley Olsen, and Tommi S. Jaakkola. 2022. Simulate Time-Integrated Coarse-Grained Molecular Dynamics with Geometric Machine Learning.” In.
Greener, Joe G., and David T. Jones. 2021. Differentiable Molecular Simulation Can Learn All the Parameters in a Coarse-Grained Force Field for Proteins.” PLOS ONE 16 (9): e0256990.
Joshi, Soumil Y., and Sanket A. Deshmukh. 2021. A Review of Advancements in Coarse-Grained Molecular Dynamics Simulations.” Molecular Simulation 47 (10-11): 786–803.
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).
Kontolati, Katiana, Darius Alix-Williams, Nicholas M. Boffi, Michael L. Falk, Chris H. Rycroft, and Michael D. Shields. 2021. Manifold Learning for Coarse-Graining Atomistic Simulations: Application to Amorphous Solids.” Acta Materialia 215 (August): 117008.
Ma, Zhan, Shu Wang, Minhee Kim, Kaibo Liu, Chun-Long Chen, and Wenxiao Pan. 2021. Transfer Learning of Memory Kernels for Transferable Coarse-Graining of Polymer Dynamics.” Soft Matter 17 (24): 5864–77.
Meng, Xuhui, Hessam Babaee, and George Em Karniadakis. 2021. Multi-Fidelity Bayesian Neural Networks: Algorithms and Applications.” Journal of Computational Physics 438 (August): 110361.
Nguyen, Danh, Lei Tao, and Ying Li. 2022. Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design.” Frontiers in Chemistry 9.
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.
Popov, Andrey Anatoliyevich. 2022. Combining Data-Driven and Theory-Guided Models in Ensemble Data Assimilation.” ETD. Virginia Tech.
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.
Wang, Jiang, Stefan Chmiela, Klaus-Robert Müller, Frank Noé, and Cecilia Clementi. 2020. Ensemble Learning of Coarse-Grained Molecular Dynamics Force Fields with a Kernel Approach.” The Journal of Chemical Physics 152 (19): 194106.
Wang, Jiang, Simon Olsson, Christoph Wehmeyer, Adrià Pérez, Nicholas E. Charron, Gianni de Fabritiis, Frank Noé, and Cecilia Clementi. 2019. Machine Learning of Coarse-Grained Molecular Dynamics Force Fields.” ACS Central Science 5 (5): 755–67.
White, Andrew D. 2021. Deep Learning for Molecules and Materials.” Living Journal of Computational Molecular Science 3 (1): 1499–99.
Ye, Huilin, Weikang Xian, and Ying Li. 2021. Machine Learning of Coarse-Grained Models for Organic Molecules and Polymers: Progress, Opportunities, and Challenges.” ACS Omega 6 (3): 1758–72.
Zammit-Mangion, Andrew, and Jonathan Rougier. 2019. Multi-Scale Process Modelling and Distributed Computation for Spatial Data,” July.

No comments yet. Why not leave one?

GitHub-flavored Markdown & a sane subset of HTML is supported.