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Achievement: Pull SharkAchievement: Pair Extraordinaire

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Hydrodynamical/README.md

Joseph K. Miller

Postdoctoral Associate in Mathematics · MIT

I study how collective behavior emerges from interacting particle systems. My work combines kinetic theory and mathematical analysis with numerical simulation, control, and formal verification. I also build benchmarks for scientific reasoning with language models.

Website · Publications · CV

Research software

Project Focus Explore
Graphon Control Neural interaction kernels and differentiable simulation for controlling collective dynamics. Paper · Experiments
Lucas–Moll Simulations Particle–PDE comparisons for a prescribed learning model, with reproducible runs and diagnostics. Figures & animations
Fermi–Ulam Stochastic particle models of wall heating and collisions; calibration and first-passage analysis. Model & methods
PDE Learning A benchmark of language-model experimental design for identifying unknown elliptic PDE coefficients. Preprint · Reproduction guide
Vlasov Mean-Field Formalization Lean 4 / Mathlib proofs of well-posedness, stability, and mean-field results for the Vlasov equation. Paper · Documentation

Methods

Kinetic equations · interacting particle systems · stochastic simulation · optimization · scientific machine learning · Lean formalization

Python / NumPy / PyTorch · Lean 4 / Mathlib

Pinned Loading

  1. Graphon_Control Graphon_Control Public

    Neural interaction kernels and differentiable particle simulations for controlling collective dynamics.

    Python

  2. Lucas-Moll-Simulations Lucas-Moll-Simulations Public

    Particle and PDE simulations of a prescribed Lucas–Moll learning model, with reproducible comparisons and visualizations.

    Python

  3. Fermi-Ulam Fermi-Ulam Public

    Stochastic particle models of Fermi–Ulam wall heating and collisions, with calibration and first-passage analysis.

    Python

  4. PDE_Learning PDE_Learning Public

    An interactive benchmark of language-model experimental design for identifying unknown elliptic PDE coefficients.

    Python

  5. Vlasov_Meanfield_Formalization Vlasov_Meanfield_Formalization Public

    Lean 4 / Mathlib formalization of Vlasov mean-field theory, with a companion paper and proof documentation.

    Lean 3 1