Engineers at the University of Pennsylvania have discovered that bubbles in everyday foams constantly shift positions while maintaining the foam's overall shape, following mathematical principles akin to those in deep learning for AI. This challenges traditional views of foams as glass-like and suggests learning behaviors may underpin diverse systems from materials to cells. The findings, published in Proceedings of the National Academy of Sciences, could inform adaptive materials and biological structures.
Foams, found in products like soap suds and mayonnaise, were long considered to mimic glass, with bubbles fixed in disordered positions. However, new computer simulations by University of Pennsylvania researchers reveal that bubbles in wet foams persistently wander through various arrangements without settling, even as the foam retains its form.
This dynamic behavior mirrors the process of deep learning in artificial intelligence systems. In AI training, parameters adjust iteratively via methods like gradient descent, avoiding overly precise fits that hinder generalization. Instead, systems explore broader regions of viable solutions. "Foams constantly reorganize themselves," noted John C. Crocker, professor of chemical and biomolecular engineering and co-senior author. "It's striking that foams and modern AI systems appear to follow the same mathematical principles."
Traditional physics modeled foam bubbles as particles rolling to low-energy states, like rocks in a valley. Yet, data from nearly two decades ago showed discrepancies. "When we actually looked at the data, the behavior of foams didn't match what the theory predicted," Crocker explained. The team applied AI-inspired optimization insights, finding bubbles linger in flat energy landscapes with multiple equivalent configurations.
Co-senior author Robert Riggleman, also in chemical and biomolecular engineering, highlighted a parallel: "The key insight was realizing that you don't actually want to push the system into the deepest possible valley." Keeping AI in such flatter areas enables better performance on new data, much like foam's ongoing motion.
The study reopens questions in foam research and extends to living systems, such as the cell cytoskeleton, which reorganizes while preserving structure. "Why the mathematics of deep learning accurately characterizes foams is a fascinating question," Crocker said. Supported by the National Science Foundation, the work involved co-authors Amruthesh Thirumalaiswamy and Clary Rodríguez-Cruz, with full details in the 2025 PNAS paper on viscous ripening foams.
