Research led by John C. Crocker, professor of chemical and biomolecular engineering at the University of Pennsylvania School of Engineering and Applied Science, is challenging long-standing assumptions about how common materials behave at the microscopic level. The work shows that foams, often thought to be structurally static once formed, are instead in constant internal motion—and that this motion follows the same mathematical principles used to train modern artificial intelligence systems.
Thirumalaiswamy, A., Rodríguez-Cruz, C., Riggleman, R. A., & Crocker, J. C. (2025). Slow relaxation and landscape-driven dynamics in viscous ripening foams. Proceedings of the National Academy of Sciences, 122(47). https://doi.org/10.1073/pnas.2518994122
Foams are familiar materials, appearing in products such as soaps, food emulsions, and industrial processing fluids. For decades, they have been modeled as glass-like systems, where microscopic components become trapped in disordered but largely immobile configurations. This view helped explain why foams appear mechanically stable over time, even though they are made of soft, rearrangeable bubbles.
John C. Crocker, professor of chemical and biomolecular engineering at the University of Pennsylvania stated,
“Why the mathematics of deep learning accurately characterizes foams is a fascinating question. It hints that these tools may be useful far outside of their original context, opening the door to entirely new lines of inquiry.”
New computational simulations suggest that this picture is incomplete. In a study published in the Proceedings of the National Academy of Sciences, Crocker and colleagues show that bubbles in wet foams never truly settle. Instead, they continue to move through a wide range of possible configurations, even when the foam’s overall shape remains unchanged.
The researchers tracked bubble motion using detailed numerical models that follow how individual bubbles exchange neighbors and reorganize. Rather than converging on a single low-energy arrangement, the system explored broad regions of its “energy landscape,” remaining dynamic without becoming unstable. This behavior directly conflicted with earlier theories that treated foams as systems that relax into fixed states.
What made the findings more striking was the mathematical framework that best described this motion. The same optimization principles underlying deep learning—the class of algorithms used to train neural networks—also explained the ongoing rearrangement of bubbles in foam. In both cases, systems evolve by gradually moving through regions where many configurations perform similarly well, rather than settling into a single optimal solution.
Robert A. Riggleman, co-senior author and professor of chemical and biomolecular engineering, explains that this perspective mirrors a key insight from machine learning. For AI models, forcing a system into the deepest possible minimum often reduces its ability to generalize. Allowing it to remain in flatter regions of the landscape leads to more robust performance. The foam simulations exhibited the same preference for these broad, shallow regions.
The study helps resolve inconsistencies that experimentalists had observed for years. Measurements of foam dynamics repeatedly showed motion that existing models could not fully explain. According to Crocker, those discrepancies were apparent nearly two decades ago, but the theoretical tools needed to interpret them only became clear after advances in machine learning theory.
Beyond foam physics, the findings suggest a broader connection between learning, physical matter, and biological organization. Many biological systems, including the cytoskeleton inside living cells, must continually rearrange themselves while maintaining overall structure. The researchers argue that similar mathematical descriptions may apply, offering a unified way to think about adaptability across disciplines.
From an engineering standpoint, the work reframes how disordered materials are understood and modeled. Rather than treating stability as the absence of motion, the study suggests that persistent, structured rearrangement may be a defining feature of resilient systems. This insight could influence how engineers design adaptive materials, soft robotics, and systems that must function reliably under changing conditions.
The research does not suggest that foams “learn” in a biological or cognitive sense. Instead, it shows that learning algorithms and physical materials can be governed by the same underlying mathematics. That shared structure may help explain why techniques developed for artificial intelligence are proving useful well beyond computing, offering new tools for understanding complex physical and biological systems.
Adrian graduated with a Masters Degree (1st Class Honours) in Chemical Engineering from Chester University along with Harris. His master’s research aimed to develop a standardadised clean water oxygenation transfer procedure to test bubble diffusers that are currently used in the wastewater industry commercial market. He has also undergone placments in both US and China primarely focused within the R&D department and is an associate member of the Institute of Chemical Engineers (IChemE).
