Quanjun Lang

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

Small noise analysis for Tikhonov and RKHS regularizations

Preprint · May 18, 2023 Link to item 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

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

Preprint · December 28, 2022 Link to item Cite

Data adaptive RKHS Tikhonov regularization for learning kernels in operators

Preprint · March 7, 2022 Link to item 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

Quanjun Lang

Selected Publications

A Unified Blockwise Measurement Design for Learning Quantum Channels and Lindbladians via Low-Rank Matrix Sensing

Self-test loss functions for learning weak-form operators and gradient flows

Learning Memory Kernels in Generalized Langevin Equations

Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel

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

Small noise analysis for Tikhonov and RKHS regularizations

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

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

Data adaptive RKHS Tikhonov regularization for learning kernels in operators

Data adaptive RKHS Tikhonov regularization for learning kernels in operators

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

Identifiability of interaction kernels in mean-field equations of interacting particles

Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles

Powers Of Generators On Dirichlet Spaces And Applications To Harnack Principles