Physics-constrained, data-driven discovery of coarse-grained dynamics
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven discovery for extract- ing governing equations by employing fine-scale simulation data. In particular, we cast the coarse-graining process under a probabilistic state-space model where the transition law dic- tates the evolution of the CG state variables and the emission law the coarse-to-fine map. The directed probabilistic graphical model implied, suggests that given values for the fine- grained (FG) variables, probabilistic inference tools must be employed to identify the cor- responding values for the CG states and to that end, we employ Stochastic Variational In- ference. We advocate a sparse Bayesian learning perspective which avoids overfitting and reveals the most salient features in the CG evolution law. The formulation adopted enables the quantification of a crucial, and often neglected, component in the CG process, i.e. the pre- dictive uncertainty due to information loss. Furthermore, it is capable of reconstructing the evolution of the full, fine-scale system. We demonstrate the efficacy of the proposed frame- work in high-dimensional systems of random walkers.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Advanced Space Mapping Technique Integrating a Shared Coarse Model for Multistate Tuning-Driven Multiphysics Optimization of Tunable Filters
This article introduces an advanced space mapping (SM) technique that applies a shared electromagnetic (EM)-based coarse model for multistate tuning-driven multiphysics optimization of tunable filters. The SM method comb…
Computational EfficiencyEmbedded-physics machine learning for coarse-graining and collective variable discovery without data
We present a novel learning framework that consistently embeds underlying physics while bypassing a significant drawback of most modern, data-driven coarse-grained approaches in the context of molecular dynamics (MD), i.…
BIG-bench Machine LearningPhysics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamics
We study the relaxation of a highly collisional, ultracold but nondegenerate gas of polar molecules. Confined within a harmonic trap, the gas is subject to fluid-gaseous coupled dynamics that lead to a breakdown of first…
FormData-Driven Discovery of Coarse-Grained Equations
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two …
BIG-bench Machine LearningEquation DiscoveryOut-of-Distribution Generalization for Neural Physics Solvers
Neural physics solvers are increasingly used in scientific discovery, given their potential for rapid in silico insights into physical, materials, or biological systems and their long-time evolution. However, poor genera…