TY - JOUR
T1 - Solving Bivariate Kinetic Equations for Polymer Diffusion Using Deep Learning
AU - Wang , Heng
AU - Deng , Weihua
JO - Journal of Machine Learning
VL - 2
SP - 215
EP - 244
PY - 2024
DA - 2024/06
SN - 3
DO - http://doi.org/10.4208/jml.240124
UR - https://global-sci.org/intro/article_detail/jml/23212.html
KW - BSDEs, Deep BSDE method, Polymer dynamics, Brownian yet non-Gaussian.
AB - <p style="text-align: justify;">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.</p>