Scientists have developed a new AI method that can work backward from patterns to uncover the hidden processes driving them.

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 ...

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

Partial differential equations (PDEs) on Riemannian manifolds extend classical Euclidean analysis by incorporating the geometric structure encoded in a smoothly varying metric. At their heart lies the ...

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

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

A ripple tells you something happened, but not exactly what. That is the core problem behind a hard class of equations that ...

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

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge. Physics contains equations that ...