08-31

Joshua Aduol FPO

Joshua Aduol will present his FPO "Integrating Physical Structure into Machine Learning: PDE Constraints and Differentiable Dynamics" on Monday, August 31, 2026 at 10:00 AM in CS 401 & Zoom.

Zoom Link: https://princeton.zoom.us/j/8051095381

The members of Joshua’s committee are as follows:
Examiners: Ryan Adams (Adviser), Szymon Rusinkiewicz, Christine Allen-Blanchette
Readers: Ryan Adams (Adviser), Peter Orbanz (University College London)

A copy of his thesis is available upon request.  Please email gradinfo@cs.princeton.edu if you would like a copy of the thesis. 

Everyone is invited to attend the talk. 

Abstract follows below:
Despite strong empirical performance, many machine learning models ignore the governing physical laws underlying the data they model. This thesis presents some techniques to address these shortcomings in two complementary directions: 1) enforcing partial differential equations (PDE) constraints in neural networks, and 2) differentiable rigid body dynamics simulation of closed-loop kinematic chains. Within these directions, we present three contributions.

In the first project, we develop a method to construct neural networks that output a time-dependent probability density and the corresponding flow field. The approach leverages recent developments in divergence-free neural networks and enables joint modeling without the need of a numerical integrator to compute one from the other. We evaluate it against continuous normalizing flows demonstrating competitive performance with improved computational efficiency.

Extending this idea, we then develop a generalization of divergence-free neural networks to enforce underdetermined linear PDE constraints. Using results from PDE theory on the invertibility of linear differential operators, we construct models that satisfy these constraints by design. This yields a flexible framework for PDE-constrained learning problems. We validate the approach against physics-informed neural network baselines demonstrating improved accuracy.

Finally, we present a differentiable rigid-body dynamics simulator that natively supports closed-loop mechanisms and enables large-scale vectorized simulation on GPUs. We describe the design principles underlying the system and demonstrate its use in learning controllers for multiple closed-loop mechanisms in parallel, as well as simulating a variety of mechanisms in parallel and comparing it to state-of-the-art differentiable simulators.

Together, these contributions advance the integration of physical structure into machine learning models, improving their consistency, efficiency, and applicability to real-world systems.