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Volume 32, Issue 2
Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow

Xiaodong Feng, Li Zeng & Tao Zhou

DOI: 10.4208/cicp.OA-2022-0090

Commun. Comput. Phys., 32 (2022), pp. 401-423.

Published online: 2022-08

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  • 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.

  • Keywords

Temporal normalizing flow, Fokker-Planck equations, adaptive density approximation.

  • AMS Subject Headings

65M75, 65C30, 68T07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-32-401, author = {Feng , XiaodongZeng , Li and Zhou , Tao}, title = {Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow}, journal = {Communications in Computational Physics}, year = {2022}, volume = {32}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0090}, url = {http://global-sci.org/intro/article_detail/cicp/20863.html} }
TY - JOUR T1 - Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow AU - Feng , Xiaodong AU - Zeng , Li AU - Zhou , Tao JO - Communications in Computational Physics VL - 2 SP - 401 EP - 423 PY - 2022 DA - 2022/08 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2022-0090 UR - https://global-sci.org/intro/article_detail/cicp/20863.html KW - Temporal normalizing flow, Fokker-Planck equations, adaptive density approximation. AB -

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.

Feng , XiaodongZeng , Li and Zhou , Tao. (2022). Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow. Communications in Computational Physics. 32 (2). 401-423. doi:10.4208/cicp.OA-2022-0090
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