Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

We propose a machine learning framework for the data-driven discovery of macroscopic
chemotactic Partial Differential Equations (PDEs)—and the closures that lead to them-from …

Agent-based models are a natural choice for modeling complex social systems. In such
models simple stochastic interaction rules for a large population of individuals on the …

Equations governing physico-chemical processes are usually known at microscopic spatial
scales, yet one suspects that there exist equations, eg, in the form of partial differential …

Large collections of coupled, heterogeneous agents can manifest complex dynamical
behavior presenting difficulties for simulation and analysis. However, if the collective …

We leverage data-driven model discovery methods to determine governing equations for the
emergent behavior of heterogeneous networked dynamical systems. Specifically, we …

Starting with sets of disorganized observations of spatially varying and temporally evolving
systems, obtained at different (also disorganized) sets of parameters, we demonstrate the …

Quantum process tomography conventionally uses a multitude of initial quantum states and
then performs state tomography on the process output. Here we propose and study an …

Our lives as eukaryotic organisms are defined by the collective behaviors of cellular
systems. Together groups of cells form intricate structures and accomplish complex tasks …

In this dissertation we develop a suite of data-driven modeling techniques for dynamical
systems by leveraging manifold learning, dimensionality reduction, and deep learning …