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Research — AID Lab, University of Rochester

ML for Dynamics

Learning of dynamics

A model with no physics inside can sometimes out-forecast one built from the governing equations, and sometimes it just parrots its context. We study machine learning for dynamical systems, from reservoir computers to foundation models to hybrid physics-ML methods, mapping where each approach genuinely works, where it quietly fails, and why.

Reservoir computingFoundation modelsZero-shot forecastingEquation discovery
Open questions
  • Can a foundation model forecast a dynamical system it has never seen?
  • When does a black-box predictor outperform a structured one — and vice versa?
  • How can we close the generalization gap of digital twins?
Selected papers
Physics of AI

Dynamics of learning

More training data should help, yet it sometimes makes a learned model worse. We treat machine learning as a physical system, where training traces a trajectory, a representation has a geometry, and learning can pass through phase transitions. This lens tells us when models generalize, when they memorize, and when they break.

Loss landscapesTraining dynamicsGeneralizationRegularization
Open questions
  • When can physics-uninformed machine-learning models extrapolate?
  • What features of a loss landscape distinguish a model that will generalize from one that will overfit?
  • How do different inductive biases change the learning dynamics?
Selected papers
Networks & Emergence

Rules of emergence

A few interacting oscillators can synchronize, split into chimeras, or even compute. We study how network topology, higher-order interactions, and the geometry of basins decide which of these behaviors a coupled system settles into. The rules fit on one line; the behavior does not.

SynchronizationHigher-order interactionsNetworksBasin geometry
Open questions
  • How do network structures shape collective dynamics?
  • What is the geometry of basins in high-dimensional networked systems?
  • Can hypergraph structure be reconstructed from observed dynamics alone?
Selected papers