Add to ORKGWe present a novel class of approximations for variational losses, being applicable for the training of physics-informed neural nets (PINNs). The loss formulation reflects classic Sobolev space theory for partial differential equations and their weak formulations. The loss computation rests on an extension of Gauss-Legendre cubatures, we term Sobolev cubatures, replacing automatic differentiation (A.D.). We prove the runtime complexity of training the resulting Soblev-PINNs (SC-PINNs) to be less than required by PINNs relying on A.D. On top of one-to-two order of magnitude speed-up the SC-PINNs are demonstrated to achieve closer solution approximations for prominent forward and inverse PDE problems than established PINNs achieve
Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accur...
A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating ...
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial d...
We present novel approximates of variational losses, being applicable for the training of physics-in...
We introduce a Robust version of the Variational Physics-Informed Neural Networks (RVPINNs) to appro...
Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE resid...
We consider the discretization of elliptic boundary-value problems by variational physics-informed n...
In this paper, we propose the physics informed adversarial training (PIAT) of neural networks for so...
We present FO-PINNs, physics-informed neural networks that are trained using the first-order formula...
Physics-informed neural networks (PINNs) have emerged as new data-driven PDE solvers for both forwar...
In an attempt to find alternatives for solving partial differential equations (PDEs)with traditional...
We propose a very general framework for deriving rigorous bounds on the approximation error for phys...
Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations...
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like ...
In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support...
Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accur...
A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating ...
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial d...
We present novel approximates of variational losses, being applicable for the training of physics-in...
We introduce a Robust version of the Variational Physics-Informed Neural Networks (RVPINNs) to appro...
Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE resid...
We consider the discretization of elliptic boundary-value problems by variational physics-informed n...
In this paper, we propose the physics informed adversarial training (PIAT) of neural networks for so...
We present FO-PINNs, physics-informed neural networks that are trained using the first-order formula...
Physics-informed neural networks (PINNs) have emerged as new data-driven PDE solvers for both forwar...
In an attempt to find alternatives for solving partial differential equations (PDEs)with traditional...
We propose a very general framework for deriving rigorous bounds on the approximation error for phys...
Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations...
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like ...
In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support...
Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accur...
A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating ...
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial d...