Deep Learning-Based Computational Method for Soft Matter Dynamics: Deep Onsager-Machlup Method (Communications in Computational Physics, 2025)
A deep learning-based computational method is proposed for soft matterdynamics – the deep Onsager-Machlup method (DOMM). It combines the brute forcesof 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 ofadmissible functions. It outperforms the Ritz-type variational method where one hasto impose carefully-chosen trial functions. This capability endows the DOMM withthe potential to solve rather complex problems in soft matter dynamics that involvemultiple physics with multiple slow variables, multiple scales, and multiple dissipative processes. Actually, the DOMM can be regarded as an extension of the deep Ritzmethod (DRM) developed by E and Yu that uses DNNs to solve static problems inphysics. In this work, as the first step, we focus on the validation of the DOMM as auseful computational method by using it to solve several typical soft matter dynamicproblems: particle diffusion in dilute solutions, and two-phase dynamics with andwithout hydrodynamics. The predicted results agree very well with the analytical solution or numerical solution from traditional computational methods. These resultsshow the accuracy and convergence of DOMM and justify it as an alternative computational method for solving soft matter dynamics.
Keywords: Deep learning; variational method; Onsager-Machlup functional; soft matter dynamics.