Related papers: Hyper-parameter tuning of physics-informed neural …

Physics-Informed Neural Networks (PINNs) are deep learning models that incorporate the governing physical laws of a system into the learning process, making them well-suited for solving complex scientific and engineering problems. Recently,…

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into…

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric…

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…

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…

Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that incorporate physical constraints. In this work, we introduce…

This paper empirically studies commonly observed training difficulties of Physics-Informed Neural Networks (PINNs) on dynamical systems. Our results indicate that fixed points which are inherent to these systems play a key role in the…

The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…

Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed to the so-called spectral bias of neural networks. To…

Despite their ubiquity, the rich physics present in a plasma sheath has inhibited the development of a generally applicable description of this critical region. The present study utilizes a physics-informed neural network (PINN) to evaluate…

Most noninvasive imaging techniques utilize electromagnetic or acoustic waves originating from multiple locations and directions to identify hidden geometrical structures. Surprisingly, it is also possible to image hidden voids and…

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…

Physics-Informed Neural Networks (PINNs) are a powerful deep learning method capable of providing solutions and parameter estimations of physical systems. Given the complexity of their neural network structure, the convergence speed is…

In this work, we have applied physics-informed neural networks (PINN) for solving mesh deformation problems. We used the collocation PINN method to capture the new positions of the vertex nodes while preserving the connectivity information.…

Signal-background classification is a central problem in High-Energy Physics (HEP), that plays a major role for the discovery of new fundamental particles. A recent method -- the Parametric Neural Network (pNN) -- leverages multiple signal…

Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from…

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their…

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…

Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for…