A Russian mathematician has developed a new method for analyzing a class of equations that underpin models in physics and ...

This repository contains code for the paper: "Enabling Local Neural Operators to perform Equation-Free System-Level Analysis" G. Fabiani, H. Vandecasteele, S. Goswami, C. Siettos, I.G. Kevrekidis ...

Abstract: Neural operators, such as graph neural operators (GNOs) and Fourier neural operators (FNOs), directly learn the mapping from any functional parametric dependence to the solution and have ...

Abstract: Solving partial differential equations is a key focus of research in scientific computing. Traditional neural operator methods often face challenges in capturing both global features and ...

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

Researchers have made a breakthrough in the ability to solve engineering problems. In a new paper published in Nature entitled, “A scalable framework for learning the geometry-dependent solution ...