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Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the…

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

The application of the Physics-Informed Neural Networks (PINNs) to forward and inverse analysis of pile-soil interaction problems is presented. The main challenge encountered in the Artificial Neural Network (ANN) modelling of pile-soil…

Physics-Informed Machine Learning (PIML) offers a powerful paradigm of integrating data with physical laws to address important scientific problems, such as parameter estimation, inferring hidden physics, equation discovery, and state…

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms,…

Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem,…

Electronic structure theory calculations offer an understanding of matter at the quantum level, complementing experimental studies in materials science and chemistry. One of the most widely used methods, density functional theory (DFT),…

Seismic inversion-including post-stack, pre-stack, and full waveform inversion is compute and memory-intensive. Recently, several approaches, including physics-informed machine learning, have been developed to address some of these…

Partial differential equations and variational problems can be solved with physics informed neural networks (PINNs). The unknown field is approximated with neural networks. Minimizing the residuals of the static Maxwell equation at…

Singular regular points often arise in differential equations describing physical phenomena such as fluid dynamics, electromagnetism, and gravitation. Traditional numerical techniques often fail or become unstable near these points,…

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…

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) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…

Hamiltonian learning (HL), enabling precise estimation of system parameters and underlying dynamics, plays a critical role in characterizing quantum systems. However, conventional HL methods face challenges in noise robustness and resource…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…