Assistant Professor of Physics, UT Austin
William Gilpin develops methods for extracting dynamical information from time-ordered measurements. The central setting is a system for which the governing state is only partially observed: an experiment may record one or a few signals even though the underlying dynamics involve many interacting variables. The resulting problems include reconstructing latent state spaces, identifying recurrent structure, forecasting future behavior, and inferring unobserved driving signals.
Time-series measurements can contain information about variables that were not measured directly because the observed signal is generated by an evolving dynamical state. Delay-coordinate methods exploit this dependence by combining a signal with time-lagged copies of itself to construct a representation of the underlying state space.
Deep reconstruction of strange attractors from time series (NeurIPS 2020) develops a learned version of this idea. The method applies an autoencoder to delay-embedded measurements and uses a latent-space criterion related to false nearest neighbors to select representations that preserve dynamical structure. It was evaluated on known chaotic systems as well as electrocardiograms, neural recordings, electricity consumption, and other empirical signals.
This approach differs from ordinary dimensionality reduction because the observed signal may have lower dimension than the hidden state. The objective is therefore to unfold information distributed across time rather than simply compress a high-dimensional observation.
A trajectory in a bounded state space repeatedly returns near previously visited states. These recurrences provide information that does not require a direct parametric model of the equations of motion. Recurrences Reveal Shared Causal Drivers of Complex Time Series (Physical Review X, 2025) uses this property to infer a hidden signal that drives several observed response time series.
The method constructs recurrence graphs for individual response signals and combines them to identify times at which multiple systems indicate a return of the unobserved driver to a similar state. Graph traversal then provides a reconstruction of the driver's temporal evolution. The analysis connects this reconstruction to skew-product dynamical systems, information transfer, percolation, and the recovery of the driver's attractor. Applications in the paper include experimental data from genomics, physiology, fluid dynamics, and ecology.
Forecast evaluation for chaotic data requires more than a single error metric. Pointwise predictions eventually diverge because of sensitivity to initial conditions, while a useful model may still reproduce invariant distributions, recurrence patterns, spectra, or attractor geometry. Gilpin's chaos benchmark work uses known nonlinear systems to compare these different aspects of forecast quality under controlled conditions.
Model scale versus domain knowledge in statistical forecasting of chaotic systems (2023) compares 24 forecasting methods on 135 chaotic systems using multiple forecast metrics. The study examines how predictive performance depends jointly on model class, data availability, and properties of the underlying system.
Zero-shot forecasting of chaotic systems (ICLR 2025) extends this framework to pretrained time-series models. These models receive a context window from a previously unseen system and predict subsequent values without parameter updates. The comparison includes both short-term trajectory error and longer-term dynamical statistics.
Time-series foundation models are pretrained on collections of sequences and then applied to new signals without task-specific training. Recent work by Gilpin and collaborators uses dynamical systems to study what these models actually do with their context.
Context parroting (ICLR 2026) identifies a simple forecasting strategy in which a model reuses similar motifs from its context. A direct non-neural implementation of this strategy provides a baseline for distinguishing pattern reuse from more elaborate learned dynamics. The analysis relates its performance to the recurrence structure and fractal dimension of chaotic attractors.
Universal redundancies in time series foundation models (2026) studies the internal components of several transformer-based forecasting models using layer and attention-head ablations and residual-stream attribution. The work reports common redundant structure across model families and links particular components to recurring forecast behaviors such as context copying and seasonality bias.
Transformers for dynamical systems learn transfer operators in-context (2026) uses a smaller controlled transformer to analyze a related mechanism. The model learns to lift a low-dimensional time series through delay embedding and to propagate information associated with persistent structures on the reconstructed dynamical manifold. This connects in-context time-series forecasting to transfer-operator descriptions of nonlinear dynamics.
Last updated August 2026.