Related papers: Physics-informed attention-based neural network fo…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

In recent years, deep learning technology has been used to solve partial differential equations (PDEs), among which the physics-informed neural networks (PINNs) emerges to be a promising method for solving both forward and inverse PDE…

Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve…

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,…

We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of…

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…

Stiff differential equations are prevalent in various scientific domains, posing significant challenges due to the disparate time scales of their components. As computational power grows, physics-informed neural networks (PINNs) have led to…

While physics-informed neural networks (PINNs) have become a popular deep learning framework for tackling forward and inverse problems governed by partial differential equations (PDEs), their performance is known to degrade when larger and…

Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…

Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with…

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

The present work is focused on exploring convergence of Physics-informed Neural Networks (PINNs) when applied to a specific class of second-order fully nonlinear Partial Differential Equations (PDEs). It is well-known that as the number of…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization…

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…

Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena,…

Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN…

The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…