opPINN: physics-informed neural network with operator learning to approximate solutions to the Fokker-Planck-Landau equation (Q2689626)

scientific article; zbMATH DE number 7662523

Language	Label	Description	Also known as
English	opPINN: physics-informed neural network with operator learning to approximate solutions to the Fokker-Planck-Landau equation	scientific article; zbMATH DE number 7662523

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instance of

scholarly article

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title

opPINN: physics-informed neural network with operator learning to approximate solutions to the Fokker-Planck-Landau equation (English)

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Journal of Computational Physics

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publication date

13 March 2023

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full work available at URL

https://arxiv.org/abs/2207.01765

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zbMATH Keywords

Fokker-Planck-Landau equation

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kinetic theory of gases

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physics-informed neural network (PINN)

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operator learning

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deep learning

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describes a project that uses

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Some a priori estimates for the homogeneous Landau equation with soft potentials

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Q3198247

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Prediction of aerodynamic flow fields using convolutional neural networks

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Conservative and entropy decaying numerical scheme for the isotropic Fokker-Planck-Landau equation

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Fast algorithms for numerical, conservative, and entropy approximations of the Fokker-Planck-Landau equation

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Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials

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Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials

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On the rate of convergence to equilibrium for the homogeneous Landau equation with soft potentials

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Random Batch Particle Methods for the Homogeneous Landau Equation

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Smoothing effects for weak solutions of the spatially homogeneous Landau-Fermi-Dirac equation for hard potentials

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A Practical Guide to Deterministic Particle Methods

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THE FOKKER-PLANCK ASYMPTOTICS OF THE BOLTZMANN COLLISION OPERATOR IN THE COULOMB CASE

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On asymptotics of the Boltzmann equation when the collisions become grazing

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Entropy dissipation estimates for the Landau equation in the Coulomb case and applications

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On the spatially homogeneous landau equation for hard potentials part i : existence, uniqueness and smoothness

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On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications

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Numerical methods for kinetic equations

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A numerical method for the accurate solution of the Fokker-Planck-Landau equation in the nonhomogeneous case

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Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential

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Well-posedness of the spatially homogeneous Landau equation for soft potentials

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Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential

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The Landau equation in a periodic box

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The Landau equation with the specular reflection boundary condition

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Solving high-dimensional partial differential equations using deep learning

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Multilayer feedforward networks are universal approximators

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Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach

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A class of asymptotic-preserving schemes for the Fokker-Planck-Landau equation

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Solving parametric PDE problems with artificial neural networks

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Neural algorithm for solving differential equations

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The model reduction of the Vlasov–Poisson–Fokker–Planck system to the Poisson–Nernst–Planck system <i>via</i> the Deep Neural Network Approach

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Multipole expansions for the Fokker-Planck-Landau operator

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Hermite spectral method for Fokker-Planck-Landau equation modeling collisional plasma

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Approximation to Singular Quadratic Collision Model in Fokker--Planck--Landau Equation

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Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer

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Numerical solution for high order differential equations using a hybrid neural network-optimization method

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Fast spectral methods for the Fokker-Planck-Landau collision operator.

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The completely conservative difference schemes for the nonlinear Landau-Fokker-Planck equation

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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DGM: a deep learning algorithm for solving partial differential equations

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On the Cauchy problem for Landau equations: Sequential stability, global existence

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On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks

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Numerical approximation of the spatially homogeneous Fokker-Planck-Landau equation

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Global in time estimates for the spatially homogeneous Landau equation with soft potentials

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Using neural networks to accelerate the solution of the Boltzmann equation

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A conservative scheme for Vlasov Poisson Landau modeling collisional plasmas

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Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification

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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2023.112031

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Sitelinks

Mathematics(1 entry)

mardi Publication:2689626