Related papers: Laplace-fPINNs: Laplace-based fractional physics-i…

This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…

Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we…

A Physics-Informed Neural Network (PINN) provides a distinct advantage by synergizing neural networks' capabilities with the problem's governing physical laws. In this study, we introduce an innovative approach for solving seepage problems…

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…

The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…

In this study, we explore the application of Physics-Informed Neural Networks (PINNs) to the analysis of bifurcation phenomena in ecological migration models. By integrating the fundamental principles of diffusion-advection-reaction…

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…

This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory…

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…

Solving inverse problems with Physics-Informed Neural Networks (PINNs) is computationally expensive for multi-query scenarios, as each new set of observed data requires a new, expensive training procedure. We present Inverse-Parameter Basis…

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…

Physics-informed neural networks (PINNs) are employed to solve the classical compressible flow problem in a converging-diverging nozzle. This problem represents a typical example described by the Euler equations, thorough understanding of…

Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify…

Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including those with limited data availability. However, solving…

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…

We propose gradient-enhanced PINNs based on transfer learning (TL-gPINNs) for inverse problems of the function coefficient discovery in order to overcome deficiency of the discrete characterization of the PDE loss in neural networks and…

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

How to solve inverse problems is the challenge of many engineering and industrial applications. Recently, physics-informed neural networks (PINNs) have emerged as a powerful approach to solve inverse problems efficiently. However, it is…

Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical…