195 citations · 196 across the 6 of their papers we have counts for
7 papers
A Mathematical Introduction to Diffusion Models
Jianfeng Lu
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 sampler…
A sharp hypocoercive entropy decay estimate for underdamped Langevin dynamics
Jianfeng Lu
We study the underdamped Langevin dynamics with invariant measure . Assume tha…
Mirror Descent for Deterministic Optimal Control
Ye Feng, Jianfeng Lu
We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration,…
Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels
Quanjun Lang, Jianfeng Lu
We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish…
A Unified Blockwise Measurement Design for Learning Quantum Channels and Lindbladians via Low-Rank Matrix Sensing
Quanjun Lang, Jianfeng Lu
Quantum superoperator learning is a pivotal task in quantum information science, enabling accurate reconstruction of unknown quantum operations from measurement data. We propose a…
Learning Memory Kernels in Generalized Langevin Equations
Quanjun Lang, Jianfeng Lu
We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation fun…
Solving parametric PDE problems with artificial neural networks
Yuehaw Khoo, Jianfeng Lu, Lexing Ying
The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random…