Boundary control of hyperbolic partial differential equations (PDEs) addresses the regulation of wave-like or transport processes through manipulations applied at the spatial domain’s limits. Such ...

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

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

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.

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

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 ...

My research interests are in applied and computational mathematics. I am interested in developing and analyzing high-order numerical methods for solving partial differential equations and fractional ...