Partial differential equations (PDEs) form the mathematical backbone for models in physics, engineering, biology and finance. They express relationships between the rates of change of a multivariable ...

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 ...

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 ...

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

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

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

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.

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 ...