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Coarse-grained models describe the macroscopic mean response of a process at large scales, which derives from stochastic processes at small scales. Common examples include accounting for velocity fluctuations in a turbulent fluid flow model and cloud evolution in climate models. Most existing techniques for constructing coarse-grained models feature ill-defined parameters whose values are arbitrarily chosen (e.g., a window size), are narrow in their applicability (e.g., only applicable to time series or spatial data), or cannot readily incorporate physics information. Here, we introduce the concept of physics-guided Gaussian process regression as a machine-learning-based coarse-graining technique that is broadly applicable and amenable to input from known physics-based relationships. Using a pair of case studies derived from molecular dynamics simulations, we demonstrate the attractive properties and superior performance of physics-guided Gaussian processes for coarse-graining relative to prevalent benchmarks. The key advantage of Gaussian-process-based coarse-graining is its ability to seamlessly integrate data-driven and physics-based information.
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Arbitrarily accurate, nonparametric coarse graining with Markov renewal processes and the Mori–Zwanzig formulation
Stochastic dynamics, such as molecular dynamics, are important in many scientific applications. However, summarizing and analyzing the results of such simulations is often challenging due to the high dimension in which simulations are carried out and, consequently, due to the very large amount of data that are typically generated. Coarse graining is a popular technique for addressing this problem by providing compact and expressive representations. Coarse graining, however, potentially comes at the cost of accuracy, as dynamical information is, in general, lost when projecting the problem in a lower-dimensional space. This article shows how to eliminate coarse-graining error using two key ideas. First, we represent coarse-grained dynamics as a Markov renewal process. Second, we outline a data-driven, non-parametric Mori–Zwanzig approach for computing jump times of the renewal process. Numerical tests on a small protein illustrate the method.
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- Award ID(s):
- 2111277
- PAR ID:
- 10557080
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- AIP Advances
- Volume:
- 13
- Issue:
- 9
- ISSN:
- 2158-3226
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0162440
