A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations (Q2072734)

scientific article; zbMATH DE number 7464752

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English	A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations	scientific article; zbMATH DE number 7464752

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instance of

scholarly article

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title

A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations (English)

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Computer Methods in Applied Mechanics and Engineering

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publication date

26 January 2022

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full work available at URL

https://arxiv.org/abs/2106.07606

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zbMATH Keywords

physics informed neural networks

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partial differential equation (PDEs)

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Allen Cahn equation

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Cahn Hilliard equation

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describes a project that uses

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Physics-informed neural networks for high-speed flows

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Inferring solutions of differential equations using noisy multi-fidelity data

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Machine learning of linear differential equations using Gaussian processes

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Hidden physics models: machine learning of nonlinear partial differential equations

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Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion

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Multi-output separable Gaussian process: towards an efficient, fully Bayesian paradigm for uncertainty quantification

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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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Q4558473

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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

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Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

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A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems

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Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks

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Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification

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Adversarial uncertainty quantification in physics-informed neural networks

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A generic physics-informed neural network-based constitutive model for soft biological tissues

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Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

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Solving parametric PDE problems with artificial neural networks

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THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES

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Computation of geometric partial differential equations and mean curvature flow

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Quasi–incompressible Cahn–Hilliard fluids and topological transitions

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Q5268640

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Exponential time differencing for stiff systems

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Introduction

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Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

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Free Energy of a Nonuniform System. I. Interfacial Free Energy

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The Cahn-Hilliard equation and some of its variants

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Basic principles and practical applications of the Cahn-Hilliard equation

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A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.CMA.2021.114474

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Sitelinks

Mathematics(1 entry)

mardi Publication:2072734