Machine Learning Talks on Campus

Model scale versus domain knowledge in long-term forecasting of chaos
William Gilpin
Assistant Professor of Physics at UT Austin. The Oden Institute for Computational Engineering & Sciences

Chaos and unpredictability are traditionally synonymous, yet large-scale statistical-learning methods have recently demonstrated surprising ability to forecast chaotic systems well beyond typical predictability horizons. I will describe my recent work evaluating forecasting methods on a large-scale dynamical systems dataset. At long forecast horizons, diverse methods—ranging from reservoir computers to neural ordinary differential equations—exhibit a universal tradeoff between inductive bias and forecast ability. In this regime, we find that classical properties like Lyapunov exponents fail to determine empirical predictability. Rather, forecast methods are limited by their ability to learn long-timescale slow manifolds associated with a system’s invariant measure. Our results inform a general view of complex dynamics as a generative process, with implications for how we construct and constrain time series models.