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Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp…

Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs), particularly in regimes where labeled data are scarce and physical constraints can be…

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…

Physics-informed neural networks (PINNs) provide a promising machine learning framework for solving partial differential equations, but their training often breaks down on challenging problems, sometimes converging to physically incorrect…

The transformative impact of machine learning, particularly Deep Learning (DL), on scientific and engineering domains is evident. In the context of computational fluid dynamics (CFD), Physics-Informed Neural Networks (PINNs) represent a…

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…

In this paper, we introduce the SPINNs (stochastic physics-informed neural networks) in a systematic manner. This provides a mathematical framework for approximating the solution of stochastic differential equations (SDEs) driven by Levy…

With the growth of deep neural networks (DNN), the number of DNN parameters has drastically increased. This makes DNN models hard to be deployed on resource-limited embedded systems. To alleviate this problem, dynamic pruning methods have…

In this paper, we present the Residual Integral Solver Network (RISN), a novel neural network architecture designed to solve a wide range of integral and integro-differential equations, including one-dimensional, multi-dimensional, ordinary…

In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it possible to robustly address multi-objective and multi-scale…

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…

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,…

Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also…

The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs…

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…