Nature

Boundary Value Problems and Partial Differential Equations

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.
GitHub

PIML4PDE: Physics-Informed Machine Learning for Solving Partial Differential Equations

The PIML4PDE framework is designed to solve Partial Differential Equations (PDEs) using Physics-Informed Machine Learning (PIML). This framework is intended for educational purposes, demonstrating ...
EurekAlert!

New 'optical neural engine’ solves partial differential equations

The researchers’ device applies principles of neural networking to an optical framework. As a wave encoded with a PDE passes through the ONE’s series of components, its properties gradually shift and ...
IEEE

Iterative Physics-Informed Neural Network for Solving Coupled Partial Differential Equations

Abstract: The numerical solution of coupled partial differential equations (PDEs) represents a significant challenge for traditional methods such as the finite element method (FEM), particularly in ...
IEEE

Partial Differential Equations Meet Deep Neural Networks: A Survey

Abstract: Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), ...
GitHub

Finite basis physics-informed neural networks (FBPINNs)

This repository allows you to solve forward and inverse problems related to partial differential equations (PDEs) using finite basis physics-informed neural networks (FBPINNs). FBPINNs divide the ...