@Article{JML-3-215,
author = {Wang , Heng and Deng , Weihua},
title = {Solving Bivariate Kinetic Equations for Polymer Diffusion Using Deep Learning},
journal = {Journal of Machine Learning},
year = {2024},
volume = {3},
number = {2},
pages = {215--244},
abstract = {<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>},
issn = {2790-2048},
doi = {https://doi.org/10.4208/jml.240124},
url = {http://global-sci.org/intro/article_detail/jml/23212.html}
}