Mohammad Rafiqul Islam
I design and analyze Langevin algorithms: Markov chain Monte Carlo methods for sampling high-dimensional distributions across networks of agents, inside constrained domains, and at higher orders of accuracy. At Iowa State I work with David P. Herzog. I earned my Ph.D. at Florida State University in 2026, advised by Lingjiong Zhu.
Research Spotlight
Constrained dynamics with singular repulsion
Collision-free stochastic particle systems inside a constrained domain, and numerical schemes that stay stable near the singularity without creating artificial collisions. Joint work with D. P. Herzog.
Decentralized Bayesian sampling
Agents on a network sample a shared posterior without pooling their data. This line of work removes network bias with EXTRA-type corrections and handles convex constraints through proximal regularization.
High-order Langevin Monte Carlo
Samplers built from \(P\)-th order Langevin dynamics through splitting and accurate integration. Their Wasserstein guarantees depend better on the dimension and the accuracy level as the order grows.
News
- Talk on scalable sampling via Langevin dynamics at the Analysis, Geometry & Probability Seminar, Iowa State.
- Joined Iowa State University as a postdoctoral research associate in probability.
- Completed my Ph.D. at Florida State: Advances in Langevin Algorithms for Decentralized, Constrained, and Accelerated Sampling.
- Received FSU’s Distinguished Teaching Assistant Award and the Tam Family Excellence in Graduate Student Research Award.
Selected papers
- Decentralized Proximal Stochastic Gradient Langevin DynamicsM. R. Islam, L. Zhu · arXiv 2026
- High-Order Langevin Monte Carlo AlgorithmsT. L. Dang, M. Gürbüzbalaban, M. R. Islam, N. Yao, L. Zhu · arXiv 2025
- Generalized EXTRA Stochastic Gradient Langevin DynamicsM. Gürbüzbalaban, M. R. Islam, X. Wang, L. Zhu · arXiv 2024
- GJR-GARCH Volatility Modeling under NIG and ANN for Predicting Top CryptocurrenciesF. Mostafa, P. Saha, M. R. Islam, N. Nguyen · J. Risk Financial Manag. 2021
Teaching
You played a large part in convincing me that I am capable of learning difficult subjects.Student evaluation, MAP 2302 Ordinary Differential Equations, Summer 2026
I have taught calculus, differential equations, precalculus, and actuarial mathematics since 2018. This fall I lead Calculus III recitations at Iowa State.