About

Matthew Dobson is an Associate Professor in the Department of Mathematics and Statistics at the University of Massachusetts Amherst. His research interests include multiscale modeling and numerical analysis. He is involved in award-winning teaching, research opportunities, and interdisciplinary programs within a diverse and inclusive community of excellence. His office is located in the Lederle Graduate Research Tower at UMass Amherst, and he can be contacted via email or phone for further academic inquiries.

Research topics

• Computer Science
• Statistical physics
• Artificial Intelligence
• Applied mathematics
• Mathematical analysis
• Mathematics
• Physics
• Sociology
• Medical education
• Engineering
• Geometry
• Psychology
• Mathematical optimization
• Quantum mechanics
• Astrophysics
• Algorithm
• Medicine
• Mathematics education

Selected publications

• What Do Bouncing Balls Tell us About Order and Chaos?

  Frontiers for Young Minds · 2026-05-20

  articleOpen accessSenior author

  Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Surprisingly, billiard systems can produce remarkably complex behaviors: some table shapes generate regular, periodic patterns, while others lead to chaotic motion that quickly becomes disordered. Scientists also study what happens when they shrink the ball down to the size of an electron—a world where quantum effects take over and the familiar rules of motion no longer apply. Ideas from billiard systems help researchers understand real-world phenomena, such as how light reflects inside microscopes, how sound travels in concert halls, and how electrons move in tiny electronic materials. In this article, we discuss billiard systems in their many forms and show how such a simple setup can reveal fundamental insights into the behavior of nature.

  PublisherOA PDFDOI

• Convergence of Nonequilibrium Langevin Dynamics for Planar Flows

  Journal of Statistical Physics · 2023-04-26

  article1st authorCorresponding
  PublisherDOI

• Convergence of Nonequilibrium Langevin Dynamics for Planar Flows

  arXiv (Cornell University) · 2022-08-30

  preprintOpen access1st authorCorresponding

  We prove that incompressible two dimensional nonequilibrium Langevin dynamics (NELD) converges exponentially fast to a steady-state limit cycle. We use automorphism remapping periodic boundary conditions (PBCs) techniques such as Lees-Edwards PBCs and Kraynik-Reinelt PBCs to treat respectively shear flow and planar elongational flow. After rewriting NELD in Lagrangian coordinates, the convergence is shown using a technique similar to [R. Joubaud, G. A. Pavliotis, and G. Stoltz,2014].

  PublisherOA PDFDOI

• An efficient data-driven solver for Fokker–Planck equations: algorithm and analysis

  Communications in Mathematical Sciences · 2022 · 13 citations

  1st authorCorresponding
  • Computer Science
  • Applied mathematics
  • Algorithm

  Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional Fokker-Planck equations proposed in [15]. Based on these results, we propose a new `block solver' for the stationary Fokker-Planck equation, which significantly improves the performance of the original algorithm. Some possible ways of reducing numerical artifacts caused by the block solver are discussed and tested with examples.

  PublisherDOI

• Undergraduate Research and Education in Quantum Machine Learning

  2021 IEEE Frontiers in Education Conference (FIE) · 2022 · 10 citations

  • Computer Science
  • Medical education
  • Sociology

  This Work-In-Progress paper describes a program in quantum machine learning launched in the academic year of 2021-22. The program engaged undergraduate students from STEM areas with faculty and industry mentors. Because of the COVID-19 conditions, this undergraduate engagement was offered in a virtual format. In 2022, some face-to-face meetings with presentations were also held. The program included: a) training in machine learning with quantum simulators, b) weekly presentations, and c) semester end presentations. The assessment of the program included surveys, interviews, and presentation observations. Challenges and opportunities from virtual engagement were also part of the assessment.

  PublisherDOI

• Simple periodic boundary conditions for molecular simulation of uniaxial flow

  Journal of Computational Physics · 2022-11-07 · 4 citations

  article1st authorCorresponding
  PublisherDOI

• Simple Periodic Boundary Conditions for Molecular Simulation of Uniaxial Flow

  arXiv (Cornell University) · 2021-10-15 · 1 citations

  preprintOpen access1st authorCorresponding

  We present rotating periodic boundary conditions (PBCs) for the simulation of nonequilibrium molecular dynamics (NEMD) under uniaxial stretching flow (USF) or biaxial stretching flow (BSF). Such nonequilibrium flows need specialized PBCs since the simulation box deforms with the background flow. The technique builds on previous models using one or lattice remappings, and is simpler than the PBCs developed for the general three dimensional flow. For general three dimensional flows, Dobson \cite{Dobson} and Hunt \cite{Hunt} proposed schemes which are not time-periodic since they use more than one automorphism remapping. This paper presents a single automorphism remapping PBCs for USF and BSF which is time periodic up to a rotation matrix and has a better minimum lattice spacing properties.

  PublisherOA PDFDOI

• Using Coupling Methods to Estimate Sample Quality of Stochastic Differential Equations

  SIAM/ASA Journal on Uncertainty Quantification · 2021-01-01 · 2 citations

  preprintOpen access1st authorCorresponding

  A probabilistic approach to estimating sample qualities of stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the distance between the invariant probability measure of a stochastic differential equation and that of its numerical approximation. In order to extend estimates of finite time truncation error to infinite time, it is crucial to know the rate of contraction of the transition kernel of the SDE. We find that suitable numerical coupling methods can effectively estimate such rate of contraction, which gives the distance between two invariant probability measures. Our algorithms are tested with several low and high dimensional numerical examples.

  PublisherOA PDFDOI

• Bereavement

  2021-11-25 · 2 citations

  book-chapterSenior author

  The term bereavement is used variously—to describe the reaction to loss, the loss itself, and as an experience more generally. Bereavement as it can be understood in terms of biological, psychological, social, and cultural contexts will also be explored and finally bereavement and its relation to trauma, and as a model for human response to adversity will be analyzed. Bereavement may also contribute significantly to human growth and development, and the strengths from grieving and mastering loss, and the internalizations of those loved, may all contribute to the character and adaptability of the individual. Bereavement in childhood may impact on development; much will depend on the continuity and security of the child’s life, and whether they will be supported in their adaptation. Studies of the early period of bereavement have shown increased adrenocortical activity among bereaved persons. Immune system changes have also been found in a number of studies that have shown decreased immunocompetence in bereaved subjects.

  PublisherDOI

• Simple Periodic Boundary Conditions for Molecular Simulation of Uniaxial Flow

  SSRN Electronic Journal · 2021-01-01

  articleOpen accessSenior author
  PublisherDOI

Recent grants

• PostDoctoral Research Fellowship

  NSF · $135k · 2009–2013

Frequent coauthors

• Brian I. O’Toole

  Rockefeller University

  34 shared

• Richard P. Marshall

  Galecto (Denmark)

  30 shared

• Frédéric Legoll

  École nationale des ponts et chaussées

  28 shared

• David Grayson

  23 shared

• Mitchell Luskin

  University of Minnesota

  23 shared

• Ralph J. Schureck

  New South Wales Institute of Psychiatry

  19 shared

• Gabriel Stoltz

  CERMICS

  16 shared

• Christoph Ortner

  16 shared