ChemE-CSE PhD Thesis Defense | Alexander Cohen

Alexander Cohen, ChemE-CSE PhD Thesis Defense Announcement

Thesis Title: Interpretable Learning and Control of Physical Dynamical Systems

Date:  Thursday, December 18, 2025
Time: 12 PM ET
Location: 66-110 / Zoom

Thesis Committee:

• Thesis supervisor: Jörn Dunkel, MathWorks Professor of Mathematics
• Thesis supervisor: Martin Z. Bazant, Chevron Professor of Chemical Engineering, Professor of Mathematics

Abstract:

The laws of physics are encoded as differential equations that describe how systems evolve
in time and space. These equations are traditionally derived by analyzing fundamental
physical interactions. However, in many settings the underlying physics is too complex
or high-dimensional to yield tractable differential equation models, resulting in partially
or completely unknown governing equations. Advances in machine learning have yielded
powerful predictive and generative models for complex and high-dimensional systems, but
applications of these techniques to scientific problems often lack interpretability and are
prone to violating physical constraints, especially when only limited data are available.
Hybrid methods that integrate physical structure with data-driven models have emerged
as a promising approach for accurate, interpretable modeling of complex physical systems.
This thesis develops frameworks for learning interpretable dynamical models by combining
first-principles structure with modern data-driven and machine learning methods. The
resulting models aim to be accurate, computationally efficient, interpretable, and useful for
prediction, control, and scientific understanding.

The first part of this thesis develops tools for modeling biophysical dynamics, with a focus
on animal motion, behavior, and neural activity. These systems are challenging to model
due to their high dimensionality, nonlinearities, and limited availability of comprehensive
datasets. To address these challenges, this thesis introduces spectral mode representations as
a low-dimensional and interpretable representation space for biological dynamics. While the
form of the models for these biological systems is unknown, general physical symmetries and
biological constraints are known. Accordingly, methods for incorporating physical constraints
into dynamical models in mode space are developed and applied to animals whose dynamics
can be effectively described by centerline motion. For linear dynamics, the constrained models
are Hermitian, and this structure is utilized to compare dynamics across species and behavioral
states. The framework is then extended to nonlinear, stochastic dynamics and neural control
to build generative models of neural activity, motion, and behavior. Learning is facilitated by
decomposing the vector field via a Helmholtz decomposition into gradient and divergence-free
components, which are optimized separately using score matching, diffusion models, and
generalized Hamiltonian dynamics. Coupling the dynamical system to neural activity enables
prediction of motion from neural signals and the design of neural control strategies for steering
motion. Applied to C. elegans, this model reproduces posture statistics across behavioral
states, captures stereotyped dynamics, and links neural activity to interpretable modes of
motion.

The second part of this thesis applies similar hybrid techniques to complex materials described by nonlinear partial differential equations (PDEs). These systems are challenging to model because key parameters and functions are often unknown and the equations are computationally intensive to simulate and optimize. To address these challenges, an open-source, GPU-accelerated framework is developed for optimization and control of phase-separating and pattern-forming PDEs, enabling efficient gradient-based optimization of arbitrary PDE parameters in complex domains. This tool is then leveraged to solve representative, experimentally relevant learning and control problems in energy and quantum materials, illustrating how physically structured optimization can be used to learn models for and control pattern formation. Building on this framework, this thesis develops methods for learning continuum models from molecular dynamics simulations of phase separation. Starting from particle-based simulations of a phase-separating Lennard–Jones fluid, coarse-grained continuum fields are constructed via diffusion-like smoothing operators and effective dynamical equations are learned in this continuum space. The coarse-graining procedure is linked to diffusion models from machine learning by demonstrating that the learned dynamics correspond to score functions of the coarse-grained distributions.

Finally, this thesis demonstrates the broader applicability of these ideas through several
collaborative projects, including models for controlling indoor airborne disease transmission
and for learning mosquito behavioral responses to multi-sensory stimuli.

Across these domains, the thesis advances a common perspective: integrating physical
structure with data-driven models yields dynamical systems that are both interpretable and
useful for prediction and control problems in many areas of science and engineering.