Related papers: Gradient Enhanced Self-Training Physics-Informed N…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…
Physics-Informed Neural Networks (PINNs) are becoming a popular method for solving PDEs, due to their mesh-free nature and their ability to handle high-dimensional problems where traditional numerical solvers often struggle. Despite their…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of physical phenomena described by partial differential equations (PDE). However, it has been observed that PINNs are difficult to train in…
Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…
We propose S$^2$GPT-PINN, a sparse and small model for solving parametric partial differential equations (PDEs). Similar to Small Language Models (SLMs), S$^2$GPT-PINN is tailored to domain-specific (families of) PDEs and characterized by…
The Burgers hierarchy consists of nonlinear evolutionary partial differential equations (PDEs) with progressively higher-order dispersive and nonlinear terms. Notable members of this hierarchy are the Burgers equation and the…
Solving Singularly Perturbed Differential Equations (SPDEs) presents challenges due to the rapid change of their solutions at the boundary layer. In this manuscript, We propose Asymptotic Physics-Informed Neural Networks (ASPINN), a…
Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network. PINNs have emerged as a new essential tool to solve various…
We implement a Physics-Informed Neural Network (PINN) for solving the two-dimensional Burgers equations. This type of model can be trained with no previous knowledge of the solution; instead, it relies on evaluating the governing equations…
The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally demanding.…
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…
The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…
"AI for Science" aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a…
Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…
Wave propagation problems are typically formulated as partial differential equations (PDEs) on unbounded domains to be solved. The classical approach to solving such problems involves truncating them to problems on bounded domains by…
Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…