Analytical solution of stochastic differential equation by multilayer perceptron neural network approximation of Fokker–Planck equation

DOI10.1002/num.22445OpenAlexW2987904136WikidataQ114235303 ScholiaQ114235303MaRDI QIDQ6071665

Mehdi Ramezani, Ali Namadchian

Publication date: 28 November 2023

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.22445

zbMATH Keywords

stochastic differential equationFokker-Planck equationneural networkBayesian regularizationLevenberg-Marquardt training algorithm

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Cites Work

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• The Fokker-Planck equation. Methods of solution and applications.
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• A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure
• A probabilistic framework for the control of systems with discrete states and stochastic excitation
• Multilayer feedforward networks are universal approximators
• Lyapunov-based model predictive control of stochastic nonlinear systems
• A two-dimensional Chebyshev wavelets approach for solving the Fokker-Planck equations of time and space fractional derivatives type with variable coefficients
• A practical difference scheme for Fokker-Planck equations
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Composite generalized Laguerre spectral method for nonlinear Fokker-Planck equations on the whole line
• OPTIMAL CONTROL OF PROBABILITY DENSITY FUNCTIONS OF STOCHASTIC PROCESSES
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

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