Year: 2025
Author: Zhihao Li, Boyi Zou, Haiqin Wang, Jian Su, Dong Wang, Xinpeng Xu
Communications in Computational Physics, Vol. 37 (2025), Iss. 2 : pp. 353–382
Abstract
A deep learning-based computational method is proposed for soft matter dynamics – the deep Onsager-Machlup method (DOMM). It combines the brute forces of deep neural networks (DNNs) with the fundamental physics principle – Onsager-Machlup variational principle (OMVP). In the DOMM, the trial solution to the dynamics is constructed by DNNs that allow us to explore a rich and complex set of admissible functions. It outperforms the Ritz-type variational method where one has to impose carefully-chosen trial functions. This capability endows the DOMM with the potential to solve rather complex problems in soft matter dynamics that involve multiple physics with multiple slow variables, multiple scales, and multiple dissipative processes. Actually, the DOMM can be regarded as an extension of the deep Ritz method (DRM) developed by E and Yu that uses DNNs to solve static problems in physics. In this work, as the first step, we focus on the validation of the DOMM as a useful computational method by using it to solve several typical soft matter dynamic problems: particle diffusion in dilute solutions, and two-phase dynamics with and without hydrodynamics. The predicted results agree very well with the analytical solution or numerical solution from traditional computational methods. These results show the accuracy and convergence of DOMM and justify it as an alternative computational method for solving soft matter dynamics.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0294
Communications in Computational Physics, Vol. 37 (2025), Iss. 2 : pp. 353–382
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Deep learning variational method Onsager-Machlup functional soft matter dynamics.