Physics-informed Karhunen-Loéve and neural network approximations for solving inverse differential equation problems (Q2671323)

scientific article

Language	Label	Description	Also known as
English	Physics-informed Karhunen-Loéve and neural network approximations for solving inverse differential equation problems	scientific article

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instance of

scholarly article

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title

Physics-informed Karhunen-Loéve and neural network approximations for solving inverse differential equation problems (English)

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author

Yanyan Li

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published in

Journal of Computational Physics

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publication date

3 June 2022

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zbMATH Keywords

physics-informed machine learning

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parameter estimation

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inverse problems

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conditional Karhunen-Loéve expansions

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deep neural networks

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describes a project that uses

PINNsNTK

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DiffSharp

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1016/j.jcp.2022.111230

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cites work

Approximate Bayesian model inversion for PDEs with heterogeneous and state-dependent coefficients

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Q4558473

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Solving and learning nonlinear PDEs with Gaussian processes

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Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes

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A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems

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Multilayer feedforward networks are universal approximators

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Conditional Simulation of Flow in Heterogeneous Porous Media with the Probabilistic Collocation Method

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Gaussian process regression and conditional polynomial chaos for parameter estimation

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Q5268658

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Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems

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Conditional stochastic simulations of flow and transport with Karhunen-Loève expansions, stochastic collocation, and sequential Gaussian simulation

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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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Advanced Lectures on Machine Learning

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Physics-informed machine learning with conditional Karhunen-Loève expansions

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Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models

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The multivariate normal distribution

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When and why PINNs fail to train: a neural tangent kernel perspective

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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

DOI

10.1016/j.jcp.2022.111230

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:2671323