Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

DOI10.1137/20M1360153zbMath1480.35377arXiv2008.10653OpenAlexW3173192644MaRDI QIDQ5004999

No author found.

Publication date: 4 August 2021

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

Full work available at URL: https://arxiv.org/abs/2008.10653

zbMATH Keywords

nonlocalitysmall dataKullback-Leibler divergenceLévy noisedeep neural networksphysics-informed learning

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Brownian motion (60J65) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Neural nets and related approaches to inference from stochastic processes (62M45) Fokker-Planck equations (35Q84)

Related Items (16)

Adaptive deep density approximation for Fokker-Planck equations ⋮ Computing the invariant distribution of randomly perturbed dynamical systems using deep learning ⋮ Extracting stochastic dynamical systems with α-stable Lévy noise from data ⋮ Learning mean-field equations from particle data using WSINDy ⋮ A machine learning method for computing quasi-potential of stochastic dynamical systems ⋮ Seq-SVF: an unsupervised data-driven method for automatically identifying hidden governing equations ⋮ Data-driven method to learn the most probable transition pathway and stochastic differential equation ⋮ Adaptive deep density approximation for fractional Fokker-Planck equations ⋮ Reservoir computing with error correction: long-term behaviors of stochastic dynamical systems ⋮ Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow ⋮ Artificial neural network solver for time-dependent Fokker-Planck equations ⋮ Detecting stochastic governing laws with observation on stationary distributions ⋮ Toward a mathematical theory of trajectory inference ⋮ Nonparametric inference of stochastic differential equations based on the relative entropy rate ⋮ Neural network stochastic differential equation models with applications to financial data forecasting ⋮ Computing high-dimensional invariant distributions from noisy data

Uses Software

• FODE
• FPINNs

Cites Work

• Unnamed Item
• Fokker-Planck equations for stochastic dynamical systems with symmetric Lévy motions
• Bandwidth selection for kernel density estimation: a review of fully automatic selectors
• Most probable dynamics of a genetic regulatory network under stable Lévy noise
• Data-driven discovery of coarse-grained equations
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Lévy Processes and Stochastic Calculus
• Solving high-dimensional partial differential equations using deep learning
• Solving Fokker-Planck equation using deep learning
• fPINNs: Fractional Physics-Informed Neural Networks
• Multivariate Density Estimation
• A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation
• Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk Minimization
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
• Variational Inference for Stochastic Differential Equations

This page was built for publication: Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks