Scientific Machine Learning

Time-series foundation models

Can pre-trained transformers forecast a chaotic system without being trained on the same system?

• Y. Zhang and W. Gilpin, Zero-shot forecasting of chaotic systems, ICLR 2025
• Y. Zhang and W. Gilpin, Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning, arXiv:2505.11349

Reservior computing

Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. I am interested in understanding the success as well as identifying limitations of RC.

• Y. Zhang and S. P. Cornelius, Catch-22s of reservoir computing, Phys. Rev. Research 5, 033213 (2023)
• Y. Zhang, E. R. Santos, and S. P. Cornelius, How more data can hurt: Instability and regularization in next-generation reservoir computing, arXiv:2407.08641

Causal inference

Can we infer causal hypergraphs from time-series data in a model-free fashion? How important are higher-order interactions in the brain?

• R. Delabays, G. De Pasquale, F. Dörfler, and Y. Zhang†, Hypergraph reconstruction from dynamics, Nat. Commun. 16, 2691 (2025)

Dynamic modes decomposition

Can DMD automatically identify glassy dynamics (e.g., algebraic relaxation) from high-dimensional data?

• Z. G. Nicolaou, H. Cho, Y. Zhang, J. N. Kutz and S. L. Brunton, Signature of glassy dynamics in dynamic modes decompositions, arXiv:2502.10918

Reinforcement learning

Can we use reinforcement learning (RL) to improve synchronization? Would the solutions found by RL be interpretable?

• Z. Chen, T. Anglea, Y. Zhang and Y. Wang, Optimal synchronization in pulse-coupled oscillator networks using reinforcement learning, PNAS Nexus 2, pgad102 (2023)