Related papers: BO-SA-PINNs: Self-adaptive physics-informed neural…

Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Based on…

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ)…

In this paper, we propose a refinement strategy to the well-known Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) based on the concept of Optimal Transport (OT). Conventional black-box PINNs…

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

In this paper, we propose a novel Physics-Informed Neural Network (PINN) framework based on the Cord\`{e}s condition for solving both linear and fully nonlinear partial differential equations (PDEs) in non-divergence form, together with…

In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide…

This paper explores the possibilities of applying physics-informed neural networks (PINNs) in topology optimization (TO) by introducing a fully self-supervised TO framework that is based on PINNs. This framework solves the forward…

Recent advances in deep learning for solving partial differential equations (PDEs) have introduced physics-informed neural networks (PINNs), which integrate machine learning with physical laws. Physics-informed convolutional neural networks…

Physics-informed neural networks (PINNs) approximate solutions of partial differential equations (PDEs) by embedding physical laws into the loss function. In parameterized PDE families, variations in coefficients or boundary/initial…

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

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 emerged as a prominent approach for solving partial differential equations (PDEs) by minimizing a combined loss function that incorporates both boundary loss and PDE residual loss. Despite their…

The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…

Learning solutions of partial differential equations (PDEs) with Physics-Informed Neural Networks (PINNs) is an attractive alternative approach to traditional solvers due to its flexibility and ease of incorporating observed data. Despite…

The performance of deep (reinforcement) learning systems crucially depends on the choice of hyperparameters. Their tuning is notoriously expensive, typically requiring an iterative training process to run for numerous steps to convergence.…

Physics-informed neural networks (PINNs) offer a powerful approach to solving partial differential equations (PDEs), which are ubiquitous in the quantitative sciences. Applied to both forward and inverse problems across various scientific…