Physical Learning in Dynamical Systems

Ziel

I propose a new paradigm in emergent adaptive matter: physical learning in dynamical systems, where physical systems autonomously adapt to changing environments through local, scalable learning processes. While physical learning was recently demonstrated in equilibrium systems, we still lack a framework for how matter can learn time-dependent tasks, such as prediction, control, and synchronization. Bridging this gap would unlock the ability to design materials and networks that learn dynamical tasks autonomously and efficiently, as if they were machine learning algorithms.
Imagine a soft robotic material that learns to walk by adapting its internal structure, not through programming, but through physical interaction with its environment. Or a living flow network like Physarum that learns to navigate and reroute resources based on changing stimuli. These are examples of dynamical learning, where both the system’s behavior and its structure evolve over time. Understanding how such systems learn could transform our approach to smart materials, neuromorphic computing, and biological physics. Building on my foundational work in equilibrium physical learning, I will develop a novel contrastive learning theory for dynamical systems, empowering diverse physical networks to learn time-dependent functions by locally contrasting dynamical trajectories. This approach reveals how physical learning emerges as a collective, non-equilibrium phenomenon, with non-reciprocity and structural adaptation as essential resources. In this project I aim to (1) identify optimal local learning rules and feedback protocols for dynamical systems, (2) understand and control the emergence of non-reciprocal interactions that balance learning efficiency, expressiveness, and energy consumption, and (3) enable networks to self-optimize their geometry and topology through unsupervised structural adaptation.

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