A metalearning approach for physics-informed neural networks (PINNs): application to parameterized PDEs (Q2681136)

scientific article

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English	A metalearning approach for physics-informed neural networks (PINNs): application to parameterized PDEs	scientific article

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instance of

scholarly article

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title

A metalearning approach for physics-informed neural networks (PINNs): application to parameterized PDEs (English)

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Journal of Computational Physics

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publication date

10 February 2023

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full work available at URL

https://arxiv.org/abs/2110.13361

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zbMATH Keywords

physics-informed neural networks (PINNs)

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parameterized PDEs

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metalearning

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surrogate modeling

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describes a project that uses

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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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Q5270493

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Meta-learning PINN loss functions

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Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

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

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PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain

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Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse 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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PPINN: parareal physics-informed neural network for time-dependent PDEs

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

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fPINNs: Fractional Physics-Informed Neural Networks

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nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

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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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Q4783863

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An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations

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Computer Model Calibration Using High-Dimensional Output

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Certified Reduced Basis Methods for Parametrized Partial Differential Equations

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Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling

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Deep coregionalization for the emulation of simulation-based spatial-temporal fields

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A radial basis function (RBF) finite difference method for the simulation of reaction–diffusion equations on stationary platelets within the augmented forcing method

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A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction-diffusion equations on surfaces

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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

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Multifidelity modeling for physics-informed neural networks (PINNs)

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Spectral and finite difference solutions of the Burgers equations

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Q3446085

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Approximation of high-dimensional parametric PDEs

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Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs

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Q3394879

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A practical guide to splines

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Monte Carlo and quasi-Monte Carlo sampling

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Hyperbolic cross approximation in infinite dimensions

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Polynomial approximation via compressed sensing of high-dimensional functions on lower sets

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Weighted Approximate Fekete Points: Sampling for Least-Squares Polynomial Approximation

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2023.111912

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Sitelinks

Mathematics(1 entry)

mardi Publication:2681136