Related papers: FO-PINNs: A First-Order formulation for Physics In…

We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through…

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…

A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schr\"odinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and…

We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the…

Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are…

The recently introduced Physics-Informed Neural Networks (PINNs) have popularized least squares formulations of both forward and inverse problems involving partial differential equations (PDEs) in strong form. We employ both Isogeometric…

Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…

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…

In many scientific and engineering (e.g., physical, biochemical, medical) practices, data generated through expensive experiments or large-scale simulations, are often sparse and noisy. Physics-informed neural network (PINN) incorporates…

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) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws directly into the loss function. However, as a fundamental optimization issue,…

Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encounted in computational science and engineering. Guided by data and physical laws, PINNs find a neural network…

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains. It is noticed, however, the performance of PINNs can vary dramatically with different sampling procedures. For…

We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator…

Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error,…