Learnable coarse-graining

Approximate meso-scale physics

August 24, 2020 — August 1, 2023

Figure 1

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 (Butler et al. 2018). 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, Behler 2016), 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 (Behler 2016) or neural networks (John and Csányi 2017; Lemke and Peter 2017; Zhang et al. 2018), have been demonstrated, there is still a need to address more complex systems and computational efficiency.

1 References

Behler. 2016. Perspective: Machine Learning Potentials for Atomistic Simulations.” The Journal of Chemical Physics.
Butler, Davies, Cartwright, et al. 2018. Machine Learning for Molecular and Materials Science.” Nature.
Chan, Cherukara, Narayanan, et al. 2019. Machine Learning Coarse Grained Models for Water.” Nature Communications.
Cutajar, Pullin, Damianou, et al. 2019. Deep Gaussian Processes for Multi-Fidelity Modeling.” arXiv:1903.07320 [Cs, Stat].
Durumeric, Charron, Templeton, et al. 2023. Machine Learned Coarse-Grained Protein Force-Fields: Are We There yet? Current Opinion in Structural Biology.
Flack. 2017. Coarse-Graining as a Downward Causation Mechanism.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
Fu, Xie, Rebello, et al. 2022. Simulate Time-Integrated Coarse-Grained Molecular Dynamics with Geometric Machine Learning.” In.
Greener, and Jones. 2021. Differentiable Molecular Simulation Can Learn All the Parameters in a Coarse-Grained Force Field for Proteins.” PLOS ONE.
Jeong, Moradzadeh, and Aluru. 2022. Extended DeepILST for Various Thermodynamic States and Applications in Coarse-Graining.” The Journal of Physical Chemistry A.
John, and Csányi. 2016. Many-Body Coarse-Grained Interactions Using Gaussian Approximation Potentials.”
———. 2017. Many-Body Coarse-Grained Interactions Using Gaussian Approximation Potentials.” The Journal of Physical Chemistry B.
Joshi, and Deshmukh. 2021. A Review of Advancements in Coarse-Grained Molecular Dynamics Simulations.” Molecular Simulation.
Köhler, Chen, Krämer, et al. 2023. Flow-Matching: Efficient Coarse-Graining of Molecular Dynamics Without Forces.” Journal of Chemical Theory and Computation.
Kontolati, Alix-Williams, Boffi, et al. 2021. Manifold Learning for Coarse-Graining Atomistic Simulations: Application to Amorphous Solids.” Acta Materialia.
Lemke, and Peter. 2017. Neural Network Based Prediction of Conformational Free Energies - A New Route Toward Coarse-Grained Simulation Models.” Journal of Chemical Theory and Computation.
Mahmoud, Masters, Lee, et al. 2022. Accurate Sampling of Macromolecular Conformations Using Adaptive Deep Learning and Coarse-Grained Representation.” Journal of Chemical Information and Modeling.
Ma, Wang, Kim, et al. 2021. Transfer Learning of Memory Kernels for Transferable Coarse-Graining of Polymer Dynamics.” Soft Matter.
Mehta, and Schwab. 2014. An Exact Mapping Between the Variational Renormalization Group and Deep Learning.”
Mohan, Lubbers, Chertkov, et al. 2023. Embedding Hard Physical Constraints in Neural Network Coarse-Graining of Three-Dimensional Turbulence.” Physical Review Fluids.
Nguyen, Tao, and Li. 2022. Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design.” Frontiers in Chemistry.
Noid. 2013. “Perspective: Coarse-Grained Models for Biomolecular Systems.” The Journal of Chemical Physics.
Perdikaris, Paris, Venturi, and Karniadakis. 2016. Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data Sets.” SIAM Journal on Scientific Computing.
Perdikaris, P., Venturi, Royset, et al. 2015. Multi-Fidelity Modelling via Recursive Co-Kriging and Gaussian–Markov Random Fields.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
Raissi, and Karniadakis. 2016. Deep Multi-Fidelity Gaussian Processes.” arXiv:1604.07484 [Cs, Stat].
Sarkar, and Joly. 2019. Multi-FIdelity Learning with Heterogeneous Domains.” In NeurIPS.
Voth. 2008. Coarse-Graining of Condensed Phase and Biomolecular Systems.
Wang, Jiang, Chmiela, Müller, et al. 2020. Ensemble Learning of Coarse-Grained Molecular Dynamics Force Fields with a Kernel Approach.” The Journal of Chemical Physics.
Wang, Wujie, and Gómez-Bombarelli. 2019. Coarse-Graining Auto-Encoders for Molecular Dynamics.” Npj Computational Materials.
Wang, Jiang, Olsson, Wehmeyer, et al. 2019. Machine Learning of Coarse-Grained Molecular Dynamics Force Fields.” ACS Central Science.
White. 2021. Deep Learning for Molecules and Materials.” Living Journal of Computational Molecular Science.
Ye, Xian, and Li. 2021. Machine Learning of Coarse-Grained Models for Organic Molecules and Polymers: Progress, Opportunities, and Challenges.” ACS Omega.
Zhang, Han, Wang, et al. 2018. DeePCG: Constructing Coarse-Grained Models via Deep Neural Networks.” The Journal of Chemical Physics.