Inverse problems in differential equations constitute a pivotal area in applied mathematics and engineering, where the aim is to deduce unknown parameters or inputs within a differential equation from ...

Inverse problems are central to modern applied mathematics, posing the challenge of deducing causes from observed effects across numerous disciplines including geophysics, medical imaging and ...

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for ...

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

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.