Despite its rapid development, Physics-Informed Neural Network (PINN)-based
computational solid mechanics is still in its infancy. In PINN, the loss function plays a critical …

The rapid growth of deep learning research, including within the field of computational
mechanics, has resulted in an extensive and diverse body of literature. To help researchers …

Abstract When using Neural Networks as trial functions to numerically solve PDEs, a key
choice to be made is the loss function to be minimised, which should ideally correspond to a …

We introduce a dynamic Deep Learning (DL) architecture based on the Finite Element
Method (FEM) to solve linear parametric Partial Differential Equations (PDEs). The …

We propose a general framework for solving forward and inverse problems constrained by
partial differential equations, where we interpolate neural networks onto finite element …

Residual minimization is a widely used technique for solving Partial Differential Equations in
variational form. It minimizes the dual norm of the residual, which naturally yields a saddle …

Abstract The Deep Fourier Residual (DFR) method is a specific type of variational physics-
informed neural network (VPINN). It provides a robust neural network-based solution to …

In this work, we develop an adversarial deep energy method (adversarial DEM) for solving
saddle point problems with electromechanical coupling. Our approach uses physics …

We propose a novel Gaussian quadrature, referred to as the learned Gaussian quadrature,
that is obtained by employing a supervised learning algorithm to find improved weights for …

In this work we investigate the numerical identification of the diffusion coefficient in elliptic
and parabolic problems using neural networks (NNs). The numerical scheme is based on …