AI method tackles one of science's hardest math problems
Peer-Reviewed Publication
Updates every hour. Last Updated: 1-May-2026 20:16 ET (2-May-2026 00:16 GMT/UTC)
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 understanding the natural world. The advance, which the researchers call “Mollifier Layers,” could benefit fields as varied as genetics and weather forecasting, because inverse PDEs help scientists work backward from observable patterns to infer the hidden dynamics that produced them.
— This study found that the dense upper canopy of the Amazon rainforest works like a vast “eavesdropping network” where animals constantly listen for predator warnings.
— When one animal senses danger, its alarm cry is quickly repeated by other species, including birds and primates. This behavior briefly links different species into a shared information network.
— Researchers found that calls from small bird species were the ones most often passed on, with other small canopy birds being the primary relayer.
Engineering researchers have developed a mathematical framework that can be used to help hunger-relief organizations get food to households that need it more efficiently than conventional methods. The advance, which has already been incorporated into an app, could also lead to improved efficiency for other businesses that face logistical challenges associated with deliveries and volunteer assignments.
Researchers have developed a new way to understand how cells survive heat stress by tracking how genes shift under changing temperatures. Studying skin fibroblasts from humans and heat-adapted one-humped camels, they created models of gene interactions using small datasets by measuring the magnitude of gene changes rather than simple on/off responses. Findings reveal that camels exhibit stronger cellular resilience than humans, offering new insight into heat adaptation and a powerful tool for studying environmental stress biology and ecological responses to environmental change.