Everyday foam reveals surprising links to how artificial intelligence learns

• What happened: Researchers at the University of Pennsylvania found that the movement of bubbles in foam follows the same mathematical patterns as deep learning in AI.

• Why it matters now: This discovery suggests that learning-like processes may be a universal principle in physical, biological, and computational systems.

• What changes for people: The research could guide development of adaptive materials and deepen understanding of living structures like cell cytoskeletons.

• Who is affected: Scientists, engineers, AI researchers, and material designers studying complex, dynamic systems.

Philadelphia, January 15: Foams—common in soap, shaving cream, whipped toppings, and emulsions like mayonnaise—may seem simple, but new research shows they are far from static. While they retain their overall shape, the bubbles inside are constantly moving, and the mathematics describing this motion mirrors the way modern artificial intelligence systems learn.

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Bubbles that never settle

Traditionally, foams were thought to behave like glass: their tiny components fixed in place. But using computer simulations, researchers observed that bubbles in wet foam never settle, instead wandering across many possible arrangements.

From a mathematical standpoint, this resembles deep learning, where AI systems continually adjust parameters rather than locking into a single solution.

"Foams constantly reorganize themselves. It's striking that foams and modern AI systems appear to follow the same mathematical principles," says John C. Crocker, Professor of Chemical and Biomolecular Engineering.

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Why traditional physics fell short

Earlier theories treated bubbles like rocks rolling downhill into stable positions, explaining why foams appear stable. However, real foam data did not fit these predictions. Discrepancies were noticed nearly 20 years ago, but only now have mathematical tools emerged to explain the behavior.

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Lessons from AI

Deep learning works by gradient descent, a step-by-step method guiding AI systems toward configurations that reduce error. Unlike old models that sought a single “deep valley” solution, modern AI performs best when parameters remain in broader, flatter regions, allowing systems to generalize.

Foam behaves similarly: bubbles never lock into deep, fixed positions but move through areas where many configurations are equally viable, echoing how AI optimizes learning.

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Broader implications

The discovery reshapes how scientists think about complex systems, from foams to living cells. The team is now investigating the cytoskeleton, the cell’s internal scaffolding, which also reorganizes continuously while maintaining structure.

"The fact that the mathematics of deep learning accurately characterizes foams hints at a shared principle of adaptability across systems," says Crocker.

This research opens doors to designing materials that adapt and respond, and could inform our understanding of biological, physical, and computational systems, showing that learning may be a universal property of dynamic matter.