Drake Brown
Applied Mathematics PhD Student · University of Utah
Building controllable generative systems through dynamics, geometry, and learning.
Learning and controlling dynamical systems
Agentic Systems / RL
Multi-agent optimization, long-horizon decision making, and adversarially robust policies.
Generative Modeling
Diffusion, flow maps, and optimal transport for learning stochastic transport between distributions.
Dynamical Systems
Neural ODEs, equation-free methods, and equivariant architectures for complex physical systems.
GNNs
Message passing, spectral theory, and geometric deep learning on structured data.
Selected work
Hover over each card to see intuition behind the dynamics.
Generative Modeling via Drift Dynamics
Controlling probability flows through learned stochastic transport processes.
Steering Generative Models
Guidance vector fields that bend generative trajectories toward target manifolds.
Neural ODEs & Three Body Problem
Equivariant neural ODEs for learning chaotic gravitational dynamics.
Epidemic Spread with Equation-Free GNNs
Graph neural networks for predicting disease propagation on dynamic topologies.
Cooperative Pursuit & Containment
Optimal control of pursuit agents corralling targets via repulsive interactions and iLQR.
Papers & preprints
Beyond Linear: A Theoretical and Empirical Analysis of Nonlinear GNNs for Community Detection
Test-Time Guidance for Flow-Based Generative Models via Parallel Tempering on Source Distributions
Explorations of Epidemiological Dynamics across Multiple Population Hubs
Manuscript under review
Timeline
Brigham Young University
GNN & Transformer Lab
Air Force Research Laboratory
AWS Serverless & API Gateway
University of Utah
AWS