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

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 ...

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 ...

Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and ...

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 ...

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 ...

Once upon a time, in the late 17th century, when mathematics was still in its infancy, two renowned mathematicians, Isaac Newton and Gottfried Wilhelm Leibniz, developed the theory of calculus. Their ...

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 ...

[Artificial Neural Networks for Solving Ordinary and Partial Differential Equations]https://www.cs.uoi.gr/~lagaris/papers/TNN-LLF.pdf), Lagaris etal, IEEE ...