Add to ORKGWe consider the approximation of weak solutions of nonlinear hyperbolic PDEs using neural networks, similar to the classical PINNs approach, but using a weak (dual) norm of the residual. This is a variant of what was termed "weak PINNs" recently. We provide some explicit computations that highlight why classical PINNs will not work well for discontinuous solutions to nonlinear hyperbolic conservation laws and we suggest some modifications to the weak PINN methodology that lead to more efficient computations and smaller errors
We present a novel class of approximations for variational losses, being applicable for the training...
The physics informed neural network (PINN) is evolving as a viable method to solve partial different...
We present FO-PINNs, physics-informed neural networks that are trained using the first-order formula...
Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accur...
We derive rigorous bounds on the error resulting from the approximation of the solution of parametri...
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial d...
We propose characteristic-informed neural networks (CINN), a simple and efficient machine learning a...
This work concerns the enrichment of Discontinuous Galerkin (DG) bases, so that the resulting scheme...
We propose an abstract framework for analyzing the convergence of least-squares methods based on res...
Hyperbolic conservation laws are an important part in classical physics to be able to mathematically...
Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE resid...
Physics-informed neural networks (PINNs) are an emerging technology in the scientific computing doma...
Physics-Informed Neural Networks (PINNs) are a new class of numerical methods for solving partial di...
In an attempt to find alternatives for solving partial differential equations (PDEs)with traditional...
Solving analytically intractable partial differential equations (PDEs) that involve at least one var...
We present a novel class of approximations for variational losses, being applicable for the training...
The physics informed neural network (PINN) is evolving as a viable method to solve partial different...
We present FO-PINNs, physics-informed neural networks that are trained using the first-order formula...
Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accur...
We derive rigorous bounds on the error resulting from the approximation of the solution of parametri...
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial d...
We propose characteristic-informed neural networks (CINN), a simple and efficient machine learning a...
This work concerns the enrichment of Discontinuous Galerkin (DG) bases, so that the resulting scheme...
We propose an abstract framework for analyzing the convergence of least-squares methods based on res...
Hyperbolic conservation laws are an important part in classical physics to be able to mathematically...
Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE resid...
Physics-informed neural networks (PINNs) are an emerging technology in the scientific computing doma...
Physics-Informed Neural Networks (PINNs) are a new class of numerical methods for solving partial di...
In an attempt to find alternatives for solving partial differential equations (PDEs)with traditional...
Solving analytically intractable partial differential equations (PDEs) that involve at least one var...
We present a novel class of approximations for variational losses, being applicable for the training...
The physics informed neural network (PINN) is evolving as a viable method to solve partial different...
We present FO-PINNs, physics-informed neural networks that are trained using the first-order formula...