Assistant Professor of Physics, UT Austin
William Gilpin studies biological systems using methods from physics, nonlinear dynamics, statistical learning, and data analysis. This work spans several scales, from fluid flows generated by cilia to ecological and gene-regulatory networks. A common theme is the search for compact physical descriptions of biological systems whose measured state is high-dimensional, partially observed, or strongly nonlinear.
Early work focused on the mechanics and fluid dynamics of ciliated microorganisms and larvae. In Vortex arrays and ciliary tangles underlie the feeding-swimming trade-off in starfish larvae (Nature Physics, 2017), William Gilpin, Vivek N. Prakash, and Manu Prakash studied the flows generated by beating ciliary bands in freely swimming starfish larvae. Experiments, particle-image velocimetry, and modeling showed that the larvae generate slowly evolving arrays of vortices and can reorganize their ciliary activity between flow states associated with feeding and swimming.
The work treated the ciliary band as an active boundary whose local deformation produces large-scale changes in the surrounding flow. Related studies examined dynamic vortex arrays and the influence of experimental boundaries on measured currents around larvae. These observations connect organismal behavior to low-Reynolds-number fluid mechanics and to the collective dynamics of many coupled cilia.
The broader physics of these systems was reviewed in The multiscale physics of cilia and flagella (Nature Reviews Physics, 2020), by William Gilpin, Matthew S. Bull, and Manu Prakash. The review connects molecular-scale force generation and filament mechanics to nonlinear oscillations, hydrodynamic coupling, synchronization, metachronal waves, and organism-scale transport. It emphasizes that cilia and flagella operate across several coupled physical scales rather than as isolated actuators.
A second line of work concerns the relationship between mechanistic dynamical models and statistical learning in biology. Learning dynamics from large biological data sets: Machine learning meets systems biology (Current Opinion in Systems Biology, 2020), by William Gilpin, Yitong Huang, and Daniel B. Forger, compares classical dynamical-systems modeling with machine-learning approaches for high-dimensional biological measurements. The review argues that the two approaches address different parts of the same problem: mechanistic models provide compact and interpretable hypotheses, while machine-learning methods can extract structure from datasets whose dimensionality makes direct model construction difficult.
This perspective also appears in later work on recovering hidden drivers and interactions from biological time series. Recurrences Reveal Shared Causal Drivers of Complex Time Series (Physical Review X, 2025) develops a reconstruction method for inferring an unobserved common driver from simultaneous recurrence events in multiple measured signals. The paper includes applications to biological and physiological data, treating latent biological regulation as a dynamical reconstruction problem rather than only a statistical association problem.
Ecological systems provide a setting in which nonlinear dynamics, optimization, and biological function can be studied together. In Optimization hardness constrains ecological transients (PLOS Computational Biology, 2025), Gilpin maps equilibration in high-dimensional ecological networks onto an analogue optimization problem. Functional redundancy among species produces poorly conditioned dynamics, separating rapid local relaxation from much slower collective equilibration.
In this description, long ecological transients are not treated as arbitrary deviations from equilibrium. Their duration and sensitivity follow from the conditioning of the underlying interaction problem. The model produces transient chaos and links dimensionality reduction to numerical preconditioning: fast components are separated from slowly relaxing directions associated with redundant ecological functions. Evolutionary simulations further show that selection for increased steady-state diversity can increase this ill-conditioning.
Modern single-cell measurements represent each cell by thousands of molecular features, creating a geometric problem as well as a biological one. In The cell as a token: high-dimensional geometry in language models and cell embeddings (Bioinformatics, 2025), Gilpin compares the geometry of single-cell embeddings with representation spaces in language models. The perspective focuses on contextual dependence, low-dimensional manifolds, interpretability methods, and the extent to which ideas developed for learned token representations can inform the construction and analysis of cell atlases.
Related work with Madison S. Krieger applies nonlinear dynamical constraints directly to gene-network inference. Interpretable gene network inference with nonlinear causality (bioRxiv, 2025) introduces the Riemannian Causal Embedding (RiCE) method for identifying directed interactions from high-dimensional time series. The method uses local geometric information from reconstructed dynamics to infer causal couplings, and is evaluated across synthetic physical systems and biological gene-expression benchmarks. The aim is to infer interaction structure while retaining parameters that have a dynamical interpretation.
A broader theoretical question is whether the large number of measured variables in modern biological datasets should be viewed mainly as an obstacle to reduction or as a source of computational capacity and robustness. The multi-author perspective Unifying theories in high-dimensional biophysics: approaches, challenges and opportunities (npj Systems Biology and Applications, 2026) surveys this issue across development, ecology, evolution, immunology, neuroscience, and systems biology.
Gilpin's contribution to that discussion draws an analogy between high-dimensional representations in biological systems and distributed representations in machine learning. Rather than assuming that biological dynamics must reduce to a small number of variables, this viewpoint asks when high dimensionality itself contributes to robustness, generalization, or the ability to support multiple functions. The resulting questions concern effective dimensionality, structured subspaces, and the mechanisms by which biological systems organize many degrees of freedom into reproducible behavior.
Last updated August 2026.