Solving Bivariate Kinetic Equations for Polymer Diffusion Using Deep Learning

Authors

  • Heng Wang
  • Weihua Deng

DOI:

https://doi.org/10.4208/jml.240124

Keywords:

BSDEs, Deep BSDE method, Polymer dynamics, Brownian yet non-Gaussian.

Abstract

In this paper, we derive a class of backward stochastic differential equations (BSDEs) for infinite-dimensionally coupled nonlinear parabolic partial differential equations, thereby extending the deep BSDE method. In addition, we introduce a class of polymer dynamics models that accompany polymerization and depolymerization reactions, and derive the corresponding Fokker-Planck equations and Feynman-Kac equations. Due to chemical reactions, the system exhibits a Brownian yet non-Gaussian phenomenon, and the resulting equations are infinitely dimensionally coupled. We solve these equations numerically through our new deep BSDE method, and also solve a class of high-dimensional nonlinear equations, which verifies the effectiveness and shows approximation accuracy of the algorithm.

Published

2024-06-27

Issue

Section

Articles