Partial Differential Equations (PDEs) are mathematical equations that involve unknown multivariate functions and their partial derivatives. They are the cornerstone of modelling a vast array of ...

Partial differential equations (PDEs) are a class of mathematical problems that represent the interplay of multiple variables, and therefore have predictive power when it comes to complex physical ...

Researchers at the University of Pennsylvania have solved a persistent obstacle in computational mathematics: how to reliably ...

Engineers at the University of Pennsylvania have developed an AI technique using 'mollifier layers' to solve complex inverse partial differential equations more efficiently and with greater stability.

A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

This addendum corrects an error in the notation of earlier versions of our paper "Partial differential equation representations of derivatives with bilateral ...

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help ...