Penn engineers use AI to solve some of science’s most difficult math problems
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 what caused it. In weather systems, biology, and materials science, researchers often have the visible result, a shifting pattern, a temperature field, a cellular structure, but not the hidden rules or forces that produced it. Engineers at the University of Pennsylvania say they have found a better way to tackle that problem with artificial intelligence. Their method, called “Mollifier Layers,” aims to make AI systems better at solving inverse partial differential equations, or inverse PDEs, especially when the data is noisy and the math gets unstable. The work, published in Transactions on Machine Learning Research and set to be presented at NeurIPS 2026, offers a different route than the one much of modern AI has taken. Instead of leaning harder on larger models and more computing power, the Penn team turned to a mathematical idea that has been around …
