Neural Parametric Fokker--Planck Equation

DOI10.1137/20M1344986zbMath1493.65132arXiv2002.11309MaRDI QIDQ5087103

Shu Liu, Wuchen Li, Hongyuan Zha, Hao-Min Zhou

Publication date: 8 July 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.11309

zbMATH Keywords

implicit Euler schemenumerical analysisoptimal transportdeep learningneural parametric Fokker-Planck equationtransport information geometry

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Applications of stochastic analysis (to PDEs, etc.) (60H30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Finite difference and finite volume methods for ordinary differential equations (65L12) Methods of ordinary differential equations applied to PDEs (35A24) Fokker-Planck equations (35Q84) PDEs on graphs and networks (ramified or polygonal spaces) (35R02) Optimal transportation (49Q22)

Related Items (3)

Stationary Density Estimation of Itô Diffusions Using Deep Learning ⋮ Adaptive deep density approximation for fractional Fokker-Planck equations ⋮ Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems

Uses Software

• Adam
• Virtual library
• BigGAN
• Wasserstein GAN

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