Year: 2022
Author: Xiaodong Feng, Li Zeng, Tao Zhou
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 401–423
Abstract
In this work, we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck (TFP) equations. It is well known that solutions of such equations are probability density functions, and thus our approach relies on modelling the target solutions with the temporal normalizing flows. The temporal normalizing flow is then trained based on the TFP loss function, without requiring any labeled data. Being a machine learning scheme, the proposed approach is mesh-free and can be easily applied to high dimensional problems. We present a variety of test problems to show the effectiveness of the learning approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0090
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 401–423
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Temporal normalizing flow Fokker-Planck equations adaptive density approximation.
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