Related papers: Hard-constrained Physics-informed Neural Networks …
We develop a new class of physics-informed neural network approximations for the stationary Oseen equations based on stability-consistent loss constructions. In contrast to standard PINN formulations, which are typically heuristic, the…
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…
We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse…
This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based…
Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…
Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in…
Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…
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…
Physics-Informed Neural Networks (PINNs) integrate physical principles into machine learning, finding wide applications in various science and engineering fields. However, solving nonlinear hyperbolic partial differential equations (PDEs)…
The concepts and techniques of physics-informed neural networks (PINNs) is studied and limitations are identified to make it efficient to approximate dynamical equations. Potential working research domains are explored for increasing the…
Physics-informed neural networks (PINNs) demonstrate promising potential in parameterized engineering turbulence optimization problems but face challenges, such as high data requirements and low computational accuracy when applied to…
The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often…
We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…
Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…
Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced…
Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, existing methods are insufficient to handle those PDE…
This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite…
In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…
Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the…
Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to…