Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning (Q6598418)

scientific article; zbMATH DE number 7906744

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English	Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning	scientific article; zbMATH DE number 7906744

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Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning (English)

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5 September 2024

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Publication

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cites work

The stability for the Cauchy problem for elliptic equations

0 references

Breaking the Curse of Dimensionality with Convex Neural Networks

0 references

Universal approximation bounds for superpositions of a sigmoidal function

0 references

Total Variation Minimization with Finite Elements: Convergence and Iterative Solution

0 references

Solving the Kolmogorov PDE by means of deep learning

0 references

Full error analysis for the training of deep neural networks

0 references

Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

0 references

Least-squares finite element methods

0 references

Q4550961

0 references

Stabilized nonconforming finite element methods for data assimilation in incompressible flows

0 references

A Regularity Theory for Static Schrödinger Equations on \(\boldsymbol{\mathbb{R}}\)<sup><i>d</i></sup> in Spectral Barron Spaces

0 references

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

0 references

Approximation by superpositions of a sigmoidal function

0 references

Q3994914

0 references

Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs

0 references

Error analysis for deep neural network approximations of parametric hyperbolic conservation laws

0 references

Error estimates for physics-informed neural networks approximating the Navier-Stokes equations

0 references

On the approximation of functions by tanh neural networks

0 references

wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws

0 references

Neural‐network‐based approximations for solving partial differential equations

0 references

An Introduction to Domain Decomposition Methods

0 references

A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

0 references

Representation formulas and pointwise properties for Barron functions

0 references

The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

0 references

The Barron space and the flow-induced function spaces for neural network models

0 references

Q5520962

0 references

Q4002879

0 references

Q5270493

0 references

Approximation rates for neural networks with encodable weights in smoothness spaces

0 references

Solving high-dimensional partial differential equations using deep learning

0 references

Spectral Methods for Time-Dependent Problems

0 references

Front tracking for hyperbolic conservation laws

0 references

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

0 references

Controllability of parabolic equations

0 references

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

0 references

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

0 references

Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

0 references

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

0 references

Q5053337

0 references

A theoretical analysis of deep neural networks and parametric PDEs

0 references

Error estimates for DeepONets: a deep learning framework in infinite dimensions

0 references

Finite Volume Methods for Hyperbolic Problems

0 references

Optimal three-ball inequalities and quantitative uniqueness for the Stokes system

0 references

On the limited memory BFGS method for large scale optimization

0 references

Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks

0 references

Deep learning observables in computational fluid dynamics

0 references

Vorticity and Incompressible Flow

0 references

Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

0 references

Estimates on the generalization error of physics-informed neural networks for approximating PDEs

0 references

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

0 references

Deep ReLU networks and high-order finite element methods

0 references

Optimal approximation of piecewise smooth functions using deep ReLU neural networks

0 references

Hidden physics models: machine learning of nonlinear partial differential equations

0 references

Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

0 references

Advanced Lectures on Machine Learning

0 references

Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ

0 references

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

0 references

Q4779819

0 references

Q2752716

0 references

Q5694789

0 references

A note on polynomial approximation in Sobolev spaces

0 references

Respecting causality for training physics-informed neural networks

0 references

Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

0 references

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

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Identifiers

zbMATH Open document ID

1546.68023

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DOI

10.1017/s0962492923000089

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6598418