https://orcid.org/0000-0001-6255-5165
Overview
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
Current Duke Appointments & Affiliations
James B. Duke Distinguished Professor of Mathematics
·
2024 - Present
Mathematics,
Trinity College of Arts & Sciences
Professor of Mathematics
·
2020 - Present
Mathematics,
Trinity College of Arts & Sciences
Associate Professor of Chemistry
·
2016 - Present
Chemistry,
Trinity College of Arts & Sciences
Professor of Physics
·
2023 - Present
Physics,
Trinity College of Arts & Sciences
Recent Scholarly Works
Log-Sobolev inequalities for boundary-driven anharmonic chains
Preprint · July 15, 2026 We study the non-equilibrium steady state of a weakly anharmonic chain of $N$ oscillators driven at its boundary by Langevin thermostats at unequal temperatures. Under a perturbative weak-anharmonicity condition, we prove a full-gradient logarithmic Sobole ... Link to item CiteA Mathematical Introduction to Diffusion Models
Preprint · July 2, 2026 These notes give a proof-oriented introduction to diffusion models from the viewpoint of sampling, tracing a single arc from classical sampling dynamics to modern diffusion samplers, their error analysis, and inference-time control. Throughout, the materia ... Link to item CiteSpace-Time Log-Sobolev Inequality and Hypocoercive Hypercontractivity for Underdamped Langevin Dynamics
Preprint · May 24, 2026 We study hypercontractivity for the underdamped Langevin dynamics with a convex confining potential. Unlike in the overdamped case, the noise acts only on the velocity variable, so the usual argument based on the logarithmic Sobolev inequality (LSI) does n ... Link to item CiteRecent Grants
Collaborative Research: RI: Medium: Machine learning for PDEs, and with PDEs
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2024 - 2028Innovation of Numerical Methods for High-Dimensional Partial Differential Equations
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2023 - 2027New computational methods to dynamically pinpointing the subregions carrying disease-associated rare variants
ResearchCo Investigator · Awarded by National Human Genome Research Institute · 2022 - 2027View All Grants
Education
Princeton University ·
2009
Ph.D.