The intersection of complex systems and artificial intelligence. We develop algorithms that extract governing equations directly from data while keeping the models interpretable.
Our research combines computational methods, applied mathematics, and machine learning to address scientific modeling challenges. We work on discovering governing equations from measurement data, incorporating physical dimensions into learning architectures, multi-scale modeling of granular materials, and agent-based simulation of social systems. We publish in applied math, computational science, and physics venues; we teach the methods in the ML for Science course sequence.
Using delay embeddings and autoencoders to jointly discover governing equations and their latent variables from high-dimensional or partial time-series observations. Demonstrated on Lorenz, Rössler, Lotka-Volterra, and a chaotic waterwheel experiment.
Building physical units and dimensional groups directly into neural architectures via constrained optimization and BuckiNet. Improves generalization across scales and preserves physical interpretability. Applied to bead on rotating hoop, laminar boundary layer, and Rayleigh-Bénard convection.
Data-driven multi-scale modeling of granular materials such as sand and powders. Explores how microstructural heterogeneity drives macroscopic behavior including reaction initiation and hotspot formation. Bridges grain-scale physics with continuum descriptions.
Modeling social behavior with agent-based frameworks embedded in graph structures, and using large language models to instantiate agent decision-making. Applications include socio-hydrological hybrid modeling for water resource management.
Research fellowship supporting the lab's activity at the intersection of applied math and machine learning.