Related papers: Approximating electromagnetic fields in discontinu…

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…

A physics-informed neural network (PINN) is developed, for the first time, to learn the time-dependent quasi-static magnetohydrodynamic (MHD) equations in axisymmetric tokamak geometry, without any experimental or synthetic data. The…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

We provide an approach enabling one to employ physics-informed neural networks (PINNs) for uncertainty quantification. Our approach is applicable to systems where observations are scarce (or even lacking), these being typical situations…

In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…

Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…

We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

This paper presents eXtended Physics-Informed Neural Network (X-PINN), a novel and robust framework for addressing fracture mechanics problems involving multiple cracks in fractured media. To address this, an energy-based loss function,…

Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren…

Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…

This paper explores the application of physics-informed neural networks (PINNs) to tackle forward problems in 3D contact mechanics, focusing on small deformation elasticity. We utilize a mixed-variable formulation, enhanced with output…

Physics--informed neural networks (PINN) have shown their potential in solving both direct and inverse problems of partial differential equations. In this paper, we introduce a PINN-based deep learning approach to reconstruct…

Simulating discontinuities is a long standing problem especially for shock waves with strong nonlinear feather. Despite being a promising method, the recently developed physics-informed neural network (PINN) is still weak for calculating…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations…

Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…