Machine learning rediscovers equations governing ocean biogeochemistry

Climate and ocean models use a series of equations to represent complex natural processes. However, the equations used in ...
Frontiers

Implementing physics-informed neural networks with deep learning for differential equations

Physics-aware machine learning integrates domain-specific physical knowledge into machine learning models, leading to the development of physics-informed neural networks (PINNs). PINNs embed physical ...
Quanta Magazine

Using AI, Mathematicians Find Hidden Glitches in Fluid Equations

Nearly 200 years ago, the physicists Claude-Louis Navier and George Gabriel Stokes put the finishing touches on a set of equations that describe how fluids swirl. And for nearly 200 years, the ...
Interesting Engineering

New AI beats supercomputers, solves math and science problems faster than ever

Engineers design safer cars, more resilient spacecraft, and stronger bridges using complex math problems that drive the underlying processes. Similarly, doctors use mathematical models to predict ...
IEEE

Solving Differential Equations using Physics-Informed Deep Equilibrium Models

Abstract: This paper introduces Physics-Informed Deep Equilibrium Models (PIDEQs) for solving initial value problems (IVPs) of ordinary differential equations (ODEs). Leveraging recent advancements in ...
GitHub

maxwell-equations

This project demonstrates the use of finite difference methods to solve Laplace's and Maxwell's equations using MATLAB. It includes a 2D solver for potential distribution and a 1D FDTD simulation for ...
Frontiers

Khalouta transform and applications to Caputo-fractional differential equations

The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both ...