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

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

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

Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...