AI & Dynamics Group
Research People Publications Join

Research

A Lorenz butterfly in fine gray lines with an amber forecast and a gray true path looping together from a small amber dot; below, the x coordinate over time, where the amber forecast lies on the gray truth for several swings before they split.
A context-parroting forecast (amber) of the Lorenz system, which copies what followed the closest match in its own past. It stays on the same wing as the truth (gray) for nearly three Lyapunov times. Method from Zhang and Gilpin, ICLR 2026.

ML for dynamics

Open questions

  • What mechanisms do foundation models use to forecast systems they have never seen?
  • When does a black-box predictor beat one that incorporates known physics?
  • How can we close the generalization gap of digital twins?

Selected papers

Thin gray contour lines of a three-well potential; two paths start from the same point at upper right, travel together, then split: the amber path settles over the right magnet and the gray one over the lower-left magnet (small circles).
Two releases of a magnetic pendulum 0.002 apart (amber, gray) travel together, then settle over different magnets (circles). Thin lines are contours of the potential. This pendulum is the test system in Zhang et al., Chaos 2025.

Physics of AI

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

Jagged gray outlines nested around an amber-outlined polygon: the basin of one twisted state of a ring of oscillators, wrapped in onion-like layers of competing basins.
A slice of state space centered on a twisted state of a ring of 83 Kuramoto oscillators, after Fig. 4 of Zhang and Strogatz, PRL 2021. Its basin (amber) is wrapped in onion-like layers; gray lines enclose states that end with at most 3, 6, and 9 fewer twists.

Networks and emergence

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