Multilevel domain decomposition-based architectures for physics-informed neural networks (Q6588267)

scientific article; zbMATH DE number 7897542

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English	Multilevel domain decomposition-based architectures for physics-informed neural networks	scientific article; zbMATH DE number 7897542

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instance of

scholarly article

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title

Multilevel domain decomposition-based architectures for physics-informed neural networks (English)

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Computer Methods in Applied Mechanics and Engineering

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publication date

15 August 2024

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zbMATH Keywords

physics-informed neural networks

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overlapping domain decomposition methods

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multilevel methods

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multi-scale modeling

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spectral bias

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forward modeling

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differential equations

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MaRDI profile type

Publication

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cites work

Scientific machine learning through physics-informed neural networks: where we are and what's next

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Solving inverse problems using data-driven models

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

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Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

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

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

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

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Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations

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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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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

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Self-adaptive physics-informed neural networks

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Machine Learning in Adaptive Domain Decomposition Methods---Predicting the Geometric Location of Constraints

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Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review

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Deep Domain Decomposition Methods: Helmholtz Equation

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Q3806726

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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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Q5270493

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On the limited memory BFGS method for large scale optimization

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Gradient Theory of Optimal Flight Paths

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

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

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Q4825126

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An Introduction to Domain Decomposition Methods

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Q4716273

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A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems

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Nonlinearly Preconditioned Inexact Newton Algorithms

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Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method

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Algorithm 832

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Identifiers

DOI

10.1016/j.cma.2024.117116

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Mathematics Subject Classification ID

65M55

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zbMATH DE Number

7897542

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Sitelinks

Mathematics(1 entry)

mardi Publication:6588267