  A deep learning-based computational method has been proposed for soft matter
dynamics -- the deep Onsager-Machlup method (DOMM), which 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 constructed using
variational formulations of physics models to solve static problems in physics
as discussed in our former work [Wang et al, Soft Matter, 2022, 18, 6015-6031].
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.
