Physics-informed Neural Networks Based on the Fokker-Planck Model for Rarefied Gas Flows
Abstract
Rarefied nonequilibrium flows are described by the Boltzmann equation, which can be solved using stochastic particle or deterministic methods. With advances in computing, data-assisted physics-informed neural networks have been widely used for flow prediction by combining governing equations with measured or computed data. Data-free PINNs do not require such training data and have been widely studied for continuum flows, but their application to rarefied flows remains limited. This study develops a data-free Fokker-Planck physics-informed neural network (FP-PINN) to describe rarefied nonequilibrium flows. The physics loss is constructed from the ellipsoidal statistical Fokker-Planck (ES-FP) equation using a velocity distribution function (VDF) closure and moment projection. The FP-PINN is evaluated for a steady one-dimensional Mach 10 normal shock. The FP-PINN results agree with the numerical ES-FP results, with errors below 1%. Compared with the particle ES-FP results, the FP-PINN predicts a sharper shock structure with errors up to 17%. This difference is attributed to the VDF closure and moment projection.
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BibTeX
@misc{kim2026physicsinformed,
title = {{Physics-informed Neural Networks Based on the Fokker-Planck Model for Rarefied Gas Flows}},
author = {Joonbeom Kim and Eunji Jun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22390},
eprint = {2610.22390},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22390},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Physics-informed Neural Networks Based on the Fokker-Planck Model for Rarefied Gas Flows
AU - Joonbeom Kim
AU - Eunji Jun
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.22390
UR - https://arxiv.org/abs/2610.22390
AB - Rarefied nonequilibrium flows are described by the Boltzmann equation, which can be solved using stochastic particle or deterministic methods. With advances in computing, data-assisted physics-informed neural networks have been widely used for flow prediction by combining governing equations with measured or computed data. Data-free PINNs do not require such training data and have been widely studied for continuum flows, but their application to rarefied flows remains limited. This study develops a data-free Fokker-Planck physics-informed neural network (FP-PINN) to describe rarefied nonequilibrium flows. The physics loss is constructed from the ellipsoidal statistical Fokker-Planck (ES-FP) equation using a velocity distribution function (VDF) closure and moment projection. The FP-PINN is evaluated for a steady one-dimensional Mach 10 normal shock. The FP-PINN results agree with the numerical ES-FP results, with errors below 1%. Compared with the particle ES-FP results, the FP-PINN predicts a sharper shock structure with errors up to 17%. This difference is attributed to the VDF closure and moment projection.
ER -