Related papers: Non-Uniqueness of Solutions in Neural Variational …

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…

Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…

It was recently shown that the loss function used for training physics-informed neural networks (PINNs) exhibits local minima at solutions corresponding to fixed points of dynamical systems. In the forward setting, where the PINN is trained…

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…

Physics-informed neural networks (PINNs) have recently emerged as a novel and popular approach for solving forward and inverse problems involving partial differential equations (PDEs). However, achieving stable training and obtaining…

Physics-Informed Neural Networks (PINNs) encounter significant training difficulties when applied to doubly-clamped beam problems, and the underlying causes are not fully understood. This study investigates the PINN loss landscape to…

Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…

Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique…

This paper explores the possibilities of applying physics-informed neural networks (PINNs) in topology optimization (TO) by introducing a fully self-supervised TO framework that is based on PINNs. This framework solves the forward…

The current work aims to incorporate physics-based loss in Physics Informed Neural Network (PINN) directly using the numerical residual obtained from the governing equation in any dicretized forward solver. PINN's major difficulties in…

In this article, we employ Chien-Physics Informed Neural Networks (C-PINNs) to obtain solutions for singularly perturbed convection-diffusion equations, reaction-diffusion equations, and their coupled forms in both one and two-dimensional…

While many recent Physics-Informed Neural Networks (PINNs) variants have had considerable success in solving Partial Differential Equations, the empirical benefits of feature mapping drawn from the broader Neural Representations research…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is challenging to solve by using conventional methods. We employ…

We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the…

The present work is focused on exploring convergence of Physics-informed Neural Networks (PINNs) when applied to a specific class of second-order fully nonlinear Partial Differential Equations (PDEs). It is well-known that as the number of…

Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible elasticity equations deteriorates as the Lam\'e coefficient $\lambda\to\infty$, or equivalently as the Poisson ratio…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…