Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning
From MaRDI portal
Publication:6598418
DOI10.1017/S0962492923000089zbMATH Open1546.68023MaRDI QIDQ6598418
Publication date: 5 September 2024
Published in: Acta Numerica (Search for Journal in Brave)
Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Deep learning observables in computational fluid dynamics
- On the limited memory BFGS method for large scale optimization
- Least-squares finite element methods
- Optimal three-ball inequalities and quantitative uniqueness for the Stokes system
- Hidden physics models: machine learning of nonlinear partial differential equations
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Solving the Kolmogorov PDE by means of deep learning
- Approximation rates for neural networks with encodable weights in smoothness spaces
- 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
- Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
- Representation formulas and pointwise properties for Barron functions
- A theoretical analysis of deep neural networks and parametric PDEs
- The Barron space and the flow-induced function spaces for neural network models
- A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
- When and why PINNs fail to train: a neural tangent kernel perspective
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- Optimal approximation of piecewise smooth functions using deep ReLU neural networks
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Vorticity and incompressible flow
- Navier-Stokes equations. Theory and numerical analysis. Repr. with corr
- Total Variation Minimization with Finite Elements: Convergence and Iterative Solution
- Spectral Methods for Time-Dependent Problems
- An Introduction to Domain Decomposition Methods
- The stability for the Cauchy problem for elliptic equations
- Universal approximation bounds for superpositions of a sigmoidal function
- Neural‐network‐based approximations for solving partial differential equations
- Finite Volume Methods for Hyperbolic Problems
- Stabilized nonconforming finite element methods for data assimilation in incompressible flows
- Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
- A note on polynomial approximation in Sobolev spaces
- Controllability of parabolic equations
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- Solving high-dimensional partial differential equations using deep learning
- Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks
- 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
- Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
- Error estimates for DeepONets: a deep learning framework in infinite dimensions
- Full error analysis for the training of deep neural networks
- Deep ReLU networks and high-order finite element methods
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
- Breaking the Curse of Dimensionality with Convex Neural Networks
- Advanced Lectures on Machine Learning
- Estimates on the generalization error of physics-informed neural networks for approximating PDEs
- A Regularity Theory for Static Schrödinger Equations on \(\boldsymbol{\mathbb{R}}\)d in Spectral Barron Spaces
- Front tracking for hyperbolic conservation laws
- Approximation by superpositions of a sigmoidal function
- On the approximation of functions by tanh neural networks
- Respecting causality for training physics-informed neural networks
- Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations
- wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws
- Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
- Error estimates for physics-informed neural networks approximating the Navier-Stokes equations
This page was built for publication: Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6598418)