Label-free learning of elliptic partial differential equation solvers with generalizability across boundary value problems (Q6146999)

scientific article; zbMATH DE number 7788072

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English	Label-free learning of elliptic partial differential equation solvers with generalizability across boundary value problems	scientific article; zbMATH DE number 7788072

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instance of

scholarly article

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title

Label-free learning of elliptic partial differential equation solvers with generalizability across boundary value problems (English)

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Computer Methods in Applied Mechanics and Engineering

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publication date

15 January 2024

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full work available at URL

https://arxiv.org/abs/2301.13165

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zbMATH Keywords

scientific machine learning

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partial differential equations

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Bayesian neural networks

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variational inference

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transfer learning

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multi-task learning

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MaRDI profile type

MaRDI publication profile

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cites work

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

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ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains

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Prediction of aerodynamic flow fields using convolutional neural networks

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Solving high-dimensional partial differential equations using deep learning

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DGM: a deep learning algorithm for solving partial differential equations

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

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Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks

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

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

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An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications

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NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations

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fPINNs: Fractional Physics-Informed Neural Networks

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PPINN: parareal physics-informed neural network for time-dependent PDEs

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Deep learning of free boundary and Stefan 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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Learning functional priors and posteriors from data and physics

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Weak adversarial networks for high-dimensional partial differential equations

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\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition

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Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains

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Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

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

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Adversarial uncertainty quantification in physics-informed neural networks

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A finite element based deep learning solver for parametric PDEs

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Q2873072

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Identifiers

arXiv ID

2301.13165

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Mathematics Subject Classification ID

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10.1016/J.CMA.2023.116214

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Sitelinks

Mathematics(1 entry)

mardi Publication:6146999