Quanjun Lang

Learning Memory Kernels in Non-Markovian Systems

I develop nonparametric methods for identifying memory kernels in generalized Langevin equations using correlation-based regression in reproducing kernel Hilbert spaces.

Related papers: SIAM J. MDS (2026), Preprint (2026)

Low-Rank Methods for Interacting Particle Systems on Graphs

I study joint inference of interaction kernels and network structure using low-rank matrix sensing techniques and mean-field limits.

Related papers: ACHA (2026), Preprint (2026)

Mean-Field Equation Learning

I study inverse problems for mean-field limits of interacting particle systems, focusing on identifiability and statistical consistency for learning interaction laws from trajectory data. My work connects mean-field analysis with scalable estimators for heterogeneous and networked populations.

Related papers: SIAM J. Sci. Comput. (2022), FoDS (2023), J. Sci. Comput. (2026)

Data-Adaptive RKHS Regularization

I develop nonparametric estimators in reproducing kernel Hilbert spaces (RKHS) with regularization operators adapted to the geometry and stability structure of dynamical systems. This yields provable guarantees in problem-tailored norms (e.g., weighted Sobolev metrics) and improves robustness for ill-posed inverse problems.

Related papers: PMLR (2022), JMLR (2024), Preprint (2023)

Quantum Channel and Superoperator Learning

I develop alternating minimization and matrix sensing methods for quantum process tomography under structural constraints.

Related papers: Preprint (2025)