Quanjun Lang
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View article: A Unified Blockwise Measurement Design for Learning Quantum Channels and Lindbladians via Low-Rank Matrix Sensing
A Unified Blockwise Measurement Design for Learning Quantum Channels and Lindbladians via Low-Rank Matrix Sensing Open
Quantum superoperator learning is a pivotal task in quantum information science, enabling accurate reconstruction of unknown quantum operations from measurement data. We propose a robust approach based on the matrix sensing techniques for …
View article: Interacting Particle Systems on Networks: Joint Inference of the Network and the Interaction Kernel
Interacting Particle Systems on Networks: Joint Inference of the Network and the Interaction Kernel Open
View article: Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals
Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals Open
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 invol…
View article: Learning Memory Kernels in Generalized Langevin Equations
Learning Memory Kernels in Generalized Langevin Equations Open
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 …
View article: Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel
Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel Open
Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. We jointly infer the weight matrix of the network and the interaction kernel, which determine respectively which agents interact with whi…
View article: Small noise analysis for Tikhonov and RKHS regularizations
Small noise analysis for Tikhonov and RKHS regularizations Open
Regularization plays a pivotal role in ill-posed machine learning and inverse problems. However, the fundamental comparative analysis of various regularization norms remains open. We establish a small noise analysis framework to assess the…
View article: Identifiability of interaction kernels in mean-field equations of interacting particles
Identifiability of interaction kernels in mean-field equations of interacting particles Open
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-dep…
View article: A Data-Adaptive Prior for Bayesian Learning of Kernels in Operators
A Data-Adaptive Prior for Bayesian Learning of Kernels in Operators Open
Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal de…
View article: Data adaptive RKHS Tikhonov regularization for learning kernels in operators
Data adaptive RKHS Tikhonov regularization for learning kernels in operators Open
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 nor…
View article: Identifiability of interaction kernels in mean-field equations of interacting particles
Identifiability of interaction kernels in mean-field equations of interacting particles Open
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-dep…
View article: Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles
Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles Open
We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with regular…
View article: Powers Of Generators On Dirichlet Spaces And Applications To Harnack Principles
Powers Of Generators On Dirichlet Spaces And Applications To Harnack Principles Open
We provide a general framework for the realization of powers or functions of suitable operators on Dirichlet spaces. The first contribution is to unify the available results dealing with specific geometries; a second one is to provide new …
View article: Powers Of Generators On Dirichlet Spaces And Applications To Harnack\n Principles
Powers Of Generators On Dirichlet Spaces And Applications To Harnack\n Principles Open
We provide a general framework for the realization of powers or functions of\nsuitable operators on Dirichlet spaces. The first contribution is to unify the\navailable results dealing with specific geometries; a second one is to provide\nn…