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Foam, a seemingly simple substance found in everything from soap suds to mayonnaise, is challenging long-held scientific beliefs and offering surprising insights into the workings of artificial intelligence and even the fundamental processes of life.
For years, scientists viewed foams as largely static structures – disordered, yet fixed in place. New research from the University of Pennsylvania, however, reveals a dynamic interior where bubbles are in constant motion, governed by mathematical principles strikingly similar to those used in deep learning, the technology powering modern AI. This discovery suggests a shared organizing principle across seemingly disparate systems and could revolutionize the design of adaptive materials and our understanding of biological structures.
Bubbles in Perpetual Motion
The groundbreaking study, published in Proceedings of the National Academy of Sciences, utilized computer simulations to track the movement of bubbles within wet foam. Researchers found that, contrary to previous assumptions, the bubbles didn’t settle into stable positions. Instead, they continuously explored a multitude of possible arrangements.
From a mathematical perspective, this behavior mirrors the iterative process of deep learning. During AI training, systems don’t lock into a single “correct” answer, but rather repeatedly adjust their internal parameters – the information defining their knowledge – to refine their performance.
“Foams constantly reorganize themselves,” explained a senior researcher involved in the study. “It’s striking that foams and modern AI systems appear to follow the same mathematical principles. Understanding why that happens is still an open question, but it could reshape how we think about adaptive materials and even living systems.”
Challenging Traditional Physics
Foams exhibit a curious duality. At the human scale, they often behave like solids, maintaining their shape and resisting compression. However, at a microscopic level, they are considered two-phase materials – bubbles suspended within a liquid or solid medium. This unique characteristic has made foams a valuable model system for studying other complex and dynamic materials, including living cells.
Traditional theories posited that foam bubbles moved across an “energy landscape,” settling into positions requiring minimal energy, much like a boulder finding its resting place in a valley. This model explained the apparent stability of formed foams. However, data collected over nearly two decades revealed a significant discrepancy between theory and reality.
“When we actually looked at the data, the behavior of foams didn’t match what the theory predicted,” said a lead investigator. “We started seeing these discrepancies nearly 20 years ago, but we didn’t yet have the mathematical tools to describe what was really happening.”
The AI Connection: A New Perspective
The key to unlocking this puzzle lay in the advancements made in artificial intelligence. Modern AI systems learn through continuous adjustments to numerical parameters during training. Early attempts focused on identifying a single, optimal solution. However, researchers discovered that pushing models too hard toward perfection resulted in fragility and poor performance on new data.
“The key insight was realizing that you don’t actually want to push the system into the deepest possible valley,” explained another senior author of the study. “Keeping it in flatter parts of the landscape, where lots of solutions perform similarly well, turns out to be what allows these models to generalize.”
When the Penn team re-examined their foam data through this lens, the connection became clear. Foam bubbles, like successful AI models, don’t seek the deepest, most stable positions. Instead, they remain in broader regions where numerous configurations are equally viable. This ongoing motion directly parallels the learning process in modern AI. The same mathematics that explains the success of deep learning also accurately describes the behavior of foam.
Implications for the Future
This research isn’t just about understanding foam; it’s about rethinking how we approach complex systems. By demonstrating that foam bubbles aren’t static but rather operate according to principles akin to learning algorithms, the study opens new avenues of inquiry.
Researchers are already revisiting the cytoskeleton, the microscopic framework within cells responsible for maintaining structure and enabling movement. Like foam, the cytoskeleton must constantly reorganize while preserving its overall integrity. .
“Why the mathematics of deep learning accurately characterizes foams is a fascinating question,” said a researcher. “It hints that these tools may be useful far outside of their original context, opening the door to entirely new lines of inquiry.”
This research was conducted at the University of Pennsylvania School of Engineering and Applied Science and supported by the National Science Foundation Division of Materials Research (1609525, 1720530). Additional co-authors include Amruthesh Thirumalaiswamy and Clary Rodríguez-Cruz.
