Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

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

Researchers at the University of Pennsylvania have introduced 'Mollifier Layers,' an AI-based mathematical approach to solve inverse partial differential equations more reliably and with less ...

A ripple tells you something happened, but not exactly what. That is the core problem behind a hard class of equations that scientists use when they try to work backward from what they can measure to ...

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