Abstract: There has been significant recent work on solving PDEs using neural networks on infinite dimensional spaces. In this talk we consider two examples. First, we prove that transformers can ...

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 ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

Partial differential equations (PDEs) are workhorses of science and engineering. They describe a vast range of phenomena, from flow around a ship’s hull, to acoustics in a concert hall, to heat ...

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 ...

ABSTRACT: This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we ...

This is a simple MOC code written in MATLAB calculating the characteristics and Mach number distribution for a simple turn. A collection of teaching scripts showing applications of partial ...

Introduction: Fractional diffusion equations offer an effective means of describing transport phenomena exhibiting abnormal diffusion pat-terns, often eluding traditional diffusion models. Methods: We ...