Research · AID Lab

ML for Dynamics

Learning of dynamics

Forecasting and discovering dynamical systems with machine learning — reservoir computers, foundation models for science, and hybrid physics-ML methods — and the failure modes and surprising capabilities of each.

Reservoir computingFoundation modelsZero-shot forecastingKoopman operators

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

Machine learning as a physical system — training as a trajectory, representations as geometry, learning as phase transition. We use this lens to explain when models generalize, when they memorize, and when adding more data makes them worse.

Loss landscapesTraining dynamicsGeneralizationReservoir computing

Open questions

→What does the geometry of a trained representation reveal about the task?
→Why does more data sometimes destabilize a learned model?
→Can dynamical-systems language explain phase transitions in learning?

Selected papers

Networks & Emergence

Rule of emergence

Simple coupling rules produce baroque collective behavior — synchronization, chimeras, even computation. We study how network topology, higher-order interactions, and the geometry of basins shape what a coupled system can do.

SynchronizationHigher-order interactionsHypergraphsBasin geometry

Open questions

→When do higher-order interactions qualitatively change collective dynamics?
→What is the geometry of basins in high-dimensional networked systems?
→Can hypergraph structure be reconstructed from observed dynamics alone?

Selected papers