Solving the inverse problem of time independent Fokker-Planck equation with a self supervised neural network method.

ABSTRACT: The Fokker-Planck equation (FPE) has been used in many important applications to study stochastic processes with the evolution of the probability density function (pdf). Previous studies on FPE mainly focus on solving the forward problem which is to predict the time-evolution of the pdf from the underlying FPE terms. However, in many applications the FPE terms are usually unknown and roughly estimated, and solving the forward problem becomes more challenging. In this work, we take a different approach of starting with the observed pdfs to recover the FPE terms using a self-supervised machine learning method. This approach, known as the inverse problem, has the advantage of requiring minimal assumptions on the FPE terms and allows data-driven scientific discovery of unknown FPE mechanisms.

SUBMITTER: Liu W 

PROVIDER: S-EPMC8324819 | biostudies-literature | 2021 Jul

REPOSITORIES: biostudies-literature