Scholars@Duke
Quanjun Lang

Quanjun Lang

William W. Elliott Assistant Research Professor of Mathematics
Mathematics

Scholarly Works

Self-Test Loss Functions for Learning Weak-Form Operators and Gradient Flows

Journal article Journal of Scientific Computing · July 1, 2026 The construction of loss functions presents a major challenge in data-driven modeling involving weak-form operators in PDEs and gradient flows, particularly due to the need to select test functions appropriately. We address this challenge by introducing se ... Full text Cite

Interacting particle systems on networks: Joint inference of the network and the interaction kernel

Journal article Applied and Computational Harmonic Analysis · May 1, 2026 Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. Given data consisting of multiple trajectories, we jointly infer the weighted network and the interaction kernel, which determine respectively which agent ... Full text Cite

Learning Memory Kernels in Generalized Langevin Equations

Journal article SIAM Journal on Mathematics of Data Science · January 1, 2026 We introduce a novel approach for learning memory kernels in generalized Langevin equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a Sobolev norm-base ... Full text Cite

Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals

Journal article Communications in Analysis and Geometry · January 1, 2025 We investigate regularity properties of some non-local equations defined on Dirichlet spaces equipped with sub-Gaussian estimates for the heat kernel associated to the generator. We prove that weak solutions for homogeneous equations involving pure powers ... Full text Cite

Learning Memory Kernels in Generalized Langevin Equations

Preprint · February 18, 2024 We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a Sobolev norm-base ... Link to item Cite

A Data-Adaptive RKHS Prior for Bayesian Learning of Kernels in Operators

Journal article Journal of Machine Learning Research · January 1, 2024 Kernels effectively represent nonlocal dependencies and are extensively employed in formulating operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal dependence, the ... Cite

IDENTIFIABILITY OF INTERACTION KERNELS IN MEAN-FIELD EQUATIONS OF INTERACTING PARTICLES

Journal article Foundations of Data Science · January 1, 2023 This study examines the identifiability of interaction kernels in mean-field equations of interacting particles or agents, an area of growing interest across various scientific and engineering fields. The main focus is identifying data-dependent function s ... Full text Cite

Data adaptive RKHS Tikhonov regularization for learning kernels in operators

Conference Proceedings of Machine Learning Research · January 1, 2022 We present DARTR: a Data Adaptive RKHS Tikhonov Regularization method for the linear inverse problem of nonparametric learning of function parameters in operators. A key ingredient is a system intrinsic data adaptive (SIDA) RKHS, whose norm restricts the l ... Cite

LEARNING INTERACTION KERNELS IN MEAN-FIELD EQUATIONS OF FIRST-ORDER SYSTEMS OF INTERACTING PARTICLES

Journal article SIAM Journal on Scientific Computing · January 1, 2022 We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for first-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with regularization, the al ... Full text Cite