A new AI breakthrough helps scientists uncover the hidden forces shaping the world around us.
Engineers at the University of Pennsylvania have developed a new AI-based technique that could help scientists solve some of the most difficult mathematical problems used to study the natural world.
The approach, called “Mollifier Layers,” is designed to handle inverse partial differential equations (PDEs), a class of equations that allows researchers to work backward from visible patterns to uncover the hidden processes that created them. These problems appear in fields ranging from genetics and materials science to weather forecasting.
“Solving an inverse problem is like looking at ripples in a pond and working backward to figure out where the pebble fell,” says Vivek Shenoy, Eduardo D. Glandt President’s Distinguished Professor in Materials Science and Engineering and senior author of a study published in Transactions on Machine Learning Research (TMLR), which will be presented at the Conference on Neural Information Processing Systems (NeurIPS 2026). “You can see the effects clearly, but the real challenge is inferring the hidden cause.”
Rather than relying on larger and more power-hungry AI systems, the researchers focused on improving the mathematics behind the process itself.
“Modern AI often advances by scaling up computation,” says Vinayak Vinayak, a doctoral candidate in MSE and co-first author of the study. “But some scientific challenges require better mathematics, not just more compute.”
