Trevor Teolis
Postdoctoral Researcher
Rice University

Trevor Teolis

Postdoctoral Researcher, Rice University
Department of Computational and Applied Mathematics & Operations Research (CMOR)
Email: tt111@rice.edu

My research develops mathematical foundations for machine learning and kinetic equations, alongside neural surrogate models for physical simulation.

Research Interests

Machine learning for physical simulation; kinetic and fluid equations; interacting particle systems; foundation models for physics; mathematical theory of transformers; neural surrogate models for wave propagation and inverse problems.

Research Overview

My research develops mathematical and computational approaches to learning the evolution of physical systems, with a focus on particle, kinetic, and fluid models.

My current theoretical work, joint with Maarten de Hoop, studies the approximation of Boltzmann-type kinetic equations by machine-learning architectures. A central idea is to represent Boltzmann dynamics through stochastic in-context maps, inspired by Nanbu particle systems and jump-process formulations. Since kinetic equations such as Boltzmann provide a phase-space description underlying fluid models, this project can also be viewed as part of a broader effort to understand foundation models for fluid and continuum dynamics. The analytical goal is to show that averages of measure-theoretic transformer maps approximate the Boltzmann solution operator in Wasserstein-type metrics.

In sampling and inference, my recent work develops SVGD for singular kernels, proving finite-particle convergence and long-time sampling results for renormalized Riesz-kernel dynamics.

Separately, I am part of a larger collaborative project on transformer dynamics, studying the long-time behavior of self-attention through interacting-particle models.

On the computational side, I develop neural surrogate models for wave propagation and subsurface imaging, with longer-term directions in full-waveform inversion and uncertainty-aware inverse problems. Across these projects, I use tools from partial differential equations, kinetic theory, stochastic processes, interacting particle systems, collective dynamics, and fluid mechanics.

Background

I received my Ph.D. in Mathematics from the University of Illinois Chicago, advised by Roman Shvydkoy. My doctoral work studied collective dynamics and interacting particle systems, including Cucker–Smale, Euler alignment, and Fokker–Planck–Navier–Stokes models, and established rigorous limits from microscopic particle dynamics to kinetic and macroscopic fluid equations.

Publications and Manuscripts

Manuscripts in Preparation

Preprints

Publications

Selected Invited Talks

Last updated: October 2026