Neural network representation of the probability density function of diffusion processes

DOI10.1063/5.0010482zbMath1456.37100arXiv2001.05437OpenAlexW3083772601WikidataQ100411991 ScholiaQ100411991MaRDI QIDQ5139752

Wayne Isaac Tan Uy, Mircea D. Grigoriu

Publication date: 10 December 2020

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.05437

zbMATH Keywords

Fokker-Planck equationneural networksGaussian white noisesPoisson white noises

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Approximation methods and numerical treatment of dynamical systems (37M99) Fokker-Planck equations (35Q84)

Related Items (2)

Stationary Density Estimation of Itô Diffusions Using Deep Learning ⋮ Numerical solution of the Fokker-Planck equation using physics-based mixture models

Uses Software

• TensorFlow
• DGM

Cites Work

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• The Fokker-Planck equation. Methods of solution and applications.
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions
• Multilayer feedforward networks are universal approximators
• DGM: a deep learning algorithm for solving partial differential equations
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Numerical methods for high-dimensional probability density function equations
• Large Sample Properties of Simulations Using Latin Hypercube Sampling
• Rigorous Analysis for Efficient Statistically Accurate Algorithms for Solving Fokker--Planck Equations in Large Dimensions
• Solving Fokker-Planck equation using deep learning
• Numerical Solution of the Fokker–Planck Equation by Finite Difference and Finite Element Methods—A Comparative Study
• Approximation by superpositions of a sigmoidal function

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