Learnable coarse-graining

Approximate meso-scale physics



The great success of statistical mechanics is that it has discovered some coarse grained representations of complicated systems, under some very specific approximation. Can we learn more general coarse-grainings from data?

I am not yet sure if this is a separate topic from multi-fidelity modeling. It does relate to learning with conservation laws.

An interesting philosophical confusion in this idea We mix together statistical mechanics, which is about randomness from many things together, with statistics, which is about uncertainty. Hijinks ensue.

The intro to a recent workshop will do to set the scene. CECAM - (Machine) learning how to coarse-grain:

Coarse-grained (CG) models aim at a reduced description of a molecular system, offering not only practical benefits, such as significant computational advantages, but also the means to effectively test what subset of degrees of freedom and interactions are sufficient to describe physical processes of interest (Noid 2013; Voth 2008). While the last few decades have yielded significant advances in the development of coarse-grained models—from foundational considerations to practical force-field parametrization algorithms and methods—a number of strong assumptions the community makes has plagued its further development. For instance, the persistent description of nonbonded interactions in terms of pairwise functions alone puts a severe bound on the quality of these models, ultimately sacrificing accuracy and transferability.

Machine learning (ML) models—a class of statistical models that systematically improve with increased training data—have recently percolated in many areas of science as a novel powerful tool [3]. While significant developments have been made in the context of applying ML in chemistry and materials science as a way to speed-up computationally-expensive quantum-chemistry calculations [4, 5, 6, 7], the progress for CG models has been much more limited, due in part to a lack of improved computational scaling. While the development of CG force fields, using either kernels [7] or neural networks [8, 9, 10], have been demonstrated, there is still a need to address more complex systems and computational efficiency.

References

Behler, Jörg. 2016. Perspective: Machine Learning Potentials for Atomistic Simulations.” The Journal of Chemical Physics 145 (17): 170901.
Butler, Keith T., Daniel W. Davies, Hugh Cartwright, Olexandr Isayev, and Aron Walsh. 2018. Machine Learning for Molecular and Materials Science.” Nature 559 (7715): 547–55.
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.
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.
John, S. T., and Gábor Csányi. 2017. Many-Body Coarse-Grained Interactions Using Gaussian Approximation Potentials.” The Journal of Physical Chemistry B 121 (48): 10934–49.
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.
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.
Lemke, Tobias, and Christine Peter. 2017. Neural Network Based Prediction of Conformational Free Energies - A New Route Toward Coarse-Grained Simulation Models.” Journal of Chemical Theory and Computation 13 (12): 6213–21.
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.
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.
Noid, William George. 2013. “Perspective: Coarse-Grained Models for Biomolecular Systems.” The Journal of Chemical Physics 139 (9): 09B201_1.
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., 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.
Raissi, Maziar, and George Karniadakis. 2016. Deep Multi-Fidelity Gaussian Processes.” arXiv:1604.07484 [Cs, Stat], April.
Sarkar, Soumalya, and Michael Joly. 2019. Multi-FIdelity Learning with Heterogeneous Domains.” In NeurIPS, 5.
Voth, Gregory A. 2008. Coarse-Graining of Condensed Phase and Biomolecular Systems. CRC press.
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.

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