A Structure Preserving Numerical Scheme for Fokker--Planck Equations of Structured Neural Networks with Learning Rules

DOI10.1137/21M1445600zbMath1506.65136arXiv2109.04667OpenAlexW4292240266WikidataQ114927584 ScholiaQ114927584MaRDI QIDQ5097595

Zhennan Zhou, Jingwei Hu, Qing He

Publication date: 25 August 2022

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.04667

zbMATH Keywords

Fokker-Planck equationmultiscale modelasymptotic preserving schemeneuron networkstructure preserving schemenonlinear noisy leaky integrate-and-fire model

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Asymptotic behavior of solutions to PDEs (35B40) Neural networks for/in biological studies, artificial life and related topics (92B20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) PDEs with randomness, stochastic partial differential equations (35R60) Positive solutions to PDEs (35B09) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Initial-boundary value problems for PDEs of mixed type (35M13) Fokker-Planck equations (35Q84)

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