Deep learning methods for partial differential equations and related parameter identification problems (Q6070739)

scientific article; zbMATH DE number 7770225

Language	Label	Description	Also known as
English	Deep learning methods for partial differential equations and related parameter identification problems	scientific article; zbMATH DE number 7770225

Statements

instance of

scholarly article

0 references

title

Deep learning methods for partial differential equations and related parameter identification problems (English)

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

24 November 2023

0 references

full work available at URL

https://arxiv.org/abs/2212.03130

0 references

zbMATH Keywords

inverse problems for PDEs

0 references

deep learning

0 references

parameter identification

0 references

neural networks

0 references

inverse problems

0 references

neural operators

0 references

MaRDI profile type

MaRDI publication profile

0 references

cites work

Networks for nonlinear diffusion problems in imaging

0 references

Solving inverse problems using data-driven models

0 references

Numerical solution of inverse problems by weak adversarial networks

0 references

Approximation and estimation bounds for artificial neural networks

0 references

Q4558473

0 references

Deep Splitting Method for Parabolic PDEs

0 references

Snapshot-Based Methods and Algorithms

0 references

Optimal Approximation with Sparsely Connected Deep Neural Networks

0 references

The Mathematical Theory of Finite Element Methods

0 references

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

0 references

Deep-HyROMnet: a deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs

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

Neural network approximation

0 references

Regularization by architecture: a deep prior approach for inverse problems

0 references

Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

0 references

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

0 references

POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition

0 references

A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs

0 references

Deep learning‐based reduced order models for the real‐time simulation of the nonlinear dynamics of microstructures

0 references

Uniform error estimates for artificial neural network approximations for heat equations

0 references

Approximation spaces of deep neural networks

0 references

Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms

0 references

Lower bounds for artificial neural network approximations: a proof that shallow neural networks fail to overcome the curse of dimensionality

0 references

Error bounds for approximations with deep ReLU neural networks in Ws,p norms

0 references

Advanced Boundary Element Methods

0 references

Stable architectures for deep neural networks

0 references

An Algorithm for the Principal Component Analysis of Large Data Sets

0 references

Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

0 references

Solving high-dimensional partial differential equations using deep learning

0 references

Non-intrusive reduced order modeling of nonlinear problems using neural networks

0 references

Multilayer feedforward networks are universal approximators

0 references

Deep backward schemes for high-dimensional nonlinear PDEs

0 references

On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

0 references

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

Finite Pointset Method for the Simulation of a Vehicle Travelling Through a Body of Water

0 references

MIONet: Learning Multiple-Input Operators via Tensor Product

0 references

Q5053337

0 references

MESHFREE simulations in car design: closing the gaps of classical simulation tools

0 references

Fluid structure interaction (FSI) in the MESHFREE finite pointset method (FPM): theory and applications

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

NETT: solving inverse problems with deep neural networks

0 references

On the limited memory BFGS method for large scale optimization

0 references

Deep Network Approximation for Smooth Functions

0 references

DeepXDE: A Deep Learning Library for Solving Differential Equations

0 references

Physics-Informed Neural Networks with Hard Constraints for Inverse Design

0 references

A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data

0 references

Navier-Stokes equations. An introduction with applications

0 references

Meshfree generalized finite difference methods in soil mechanics. II: Numerical results

0 references

Meshfree generalized finite difference methods in soil mechanics. I: Theory

0 references

fPINNs: Fractional Physics-Informed Neural Networks

0 references

Optimal approximation of piecewise smooth functions using deep ReLU neural networks

0 references

Q4938227

0 references

Deep Hidden Physics Models: Deep 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

Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems

0 references

Deep neural networks motivated by partial differential equations

0 references

Q3529234

0 references

Provable approximation properties for deep neural networks

0 references

DGM: a deep learning algorithm for solving partial differential equations

0 references

Q4663944

0 references

Q3558349

0 references

The universal approximation theorem for complex-valued neural networks

0 references

On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks

0 references

Improved architectures and training algorithms for deep operator networks

0 references

Error bounds for approximations with deep ReLU networks

0 references

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

0 references

Nonlocal kernel network (NKN): a stable and resolution-independent deep neural network

0 references

Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

0 references

Weak adversarial networks for high-dimensional partial differential equations

0 references

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

0 references

Universality of deep convolutional neural networks

0 references

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

0 references

Identifiers

zbMATH Open document ID

1527.35501

0 references

arXiv ID

2212.03130

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

10.1088/1361-6420/ACE9D4

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:6070739