Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

Parallel computing for differential equations has emerged as a critical field in computational science, enabling the efficient simulation of complex physical systems governed by ordinary and partial ...

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

The team has improved the capabilities of physics-informed neural networks (PINNs), a type of artificial intelligence that incorporates physical laws into the learning process. Researchers from the ...

A team of engineers has proven that their analog computing device, called a memristor, can complete complex, scientific computing tasks while bypassing the limitations of digital computing. A team of ...

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.

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...