Add to ORKGWe propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physics-informed neural networks based on strong and variational formulations
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of ...
Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recen...
We present a novel class of approximations for variational losses, being applicable for the training...
When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be made is...
We analyze neural network solutions to partial differential equations obtained with Physics Informed...
Neural networks have been very successful in many applications; we often, however, lack a theoretica...
Recent works have shown that deep neural networks can be employed to solve partial differential equa...
Recent works have shown that deep neural networks can be employed to solve partial differential equa...
We introduce a Robust version of the Variational Physics-Informed Neural Networks (RVPINNs) to appro...
Recently, neural networks have been widely applied for solving partial differential equations (PDEs)...
We consider the discretization of elliptic boundary-value problems by variational physics-informed n...
We consider the approximation of weak solutions of nonlinear hyperbolic PDEs using neural networks, ...
There is tremendous potential in using neural networks to optimize numerical methods. In this paper,...
Physics Informed Neural Networks (PINNs) have recently gained popularity for solving partial differe...
Residual minimization is a widely used technique for solving Partial Differential Equations in varia...
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of ...
Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recen...
We present a novel class of approximations for variational losses, being applicable for the training...
When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be made is...
We analyze neural network solutions to partial differential equations obtained with Physics Informed...
Neural networks have been very successful in many applications; we often, however, lack a theoretica...
Recent works have shown that deep neural networks can be employed to solve partial differential equa...
Recent works have shown that deep neural networks can be employed to solve partial differential equa...
We introduce a Robust version of the Variational Physics-Informed Neural Networks (RVPINNs) to appro...
Recently, neural networks have been widely applied for solving partial differential equations (PDEs)...
We consider the discretization of elliptic boundary-value problems by variational physics-informed n...
We consider the approximation of weak solutions of nonlinear hyperbolic PDEs using neural networks, ...
There is tremendous potential in using neural networks to optimize numerical methods. In this paper,...
Physics Informed Neural Networks (PINNs) have recently gained popularity for solving partial differe...
Residual minimization is a widely used technique for solving Partial Differential Equations in varia...
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of ...
Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recen...
We present a novel class of approximations for variational losses, being applicable for the training...