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brownthesr/README.md

Drake Brown

Applied Mathematics PhD @ University of Utah. Previously BS Computational Mathematics @ BYU.

Building controllable generative systems through dynamics, geometry, and learning — generative models, neural ODEs, GNNs, equivariant deep learning, optimal control, and agentic systems.

Selected work

  • Beyond Linear: Nonlinear GNNs for Community Detection — theory + experiments linking graph structure to GNN performance and recoverability. SIAM J. Applied Mathematics, in press (2026). Co-first author. [code]
  • Test-Time Guidance for Flow-Based Generative Models via Parallel Tempering — steering pretrained generators via parallel-tempering MCMC over source latents. ICML 2026. [paper] · [code]
  • Optimal Control Strategies for Multi-Agent Sheep Herding — iLQR for cooperative pursuit and containment under nonlinear repulsive dynamics. First author. [arXiv:2510.25115]
  • Explorations of Epidemiological Dynamics across Multiple Population Hubs — equation-free modeling of disease spread on adaptive contact networks. First author. [arXiv:2510.25085]

Currently

PhD student at Utah working on accelerated training for one-step generative models, steering pretrained generators via parallel-tempering MCMC over source latents, and equivariant neural ODEs for chaotic dynamical systems. Incoming Applied Scientist Intern @ AWS (2026).

Background

  • Lead Research Assistant, GNN & Transformer Lab @ BYU (2022–25)
  • Computer Vision Intern, Air Force Research Laboratory (2023)
  • Software Engineer Intern, AWS Serverless & API Gateway (2024–25)

Pinned Loading

  1. Utah-Math-Data-Science/SPT Utah-Math-Data-Science/SPT Public

    Python

  2. Synthetic-Graphs Synthetic-Graphs Public

    We are studying the performance of various GNN architectures on Synthetic Graphs

    Python 1

  3. Optimal_Paths Optimal_Paths Public

    Here we are exploring what are the optimal path configurations for multiple objects routing for a destination

    Python 2

  4. three_body three_body Public

    Learning three-body gravitational dynamics with symmetry-constrained neural networks. Hamiltonian Neural Networks and equivariant Neural ODEs that enforce translational, rotational, and permutation…

    Jupyter Notebook

  5. Exegesis-of-Ancient-Texts Exegesis-of-Ancient-Texts Public

    We perform a machine-learning guided analysis of ancient religious texts. We find that deep learning models, such as RoBERTa and T5, are able to identify theme and even authorship.

    Python 3