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pro vyhledávání: '"Lang, Quanjun"'
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 p
Externí odkaz:
http://arxiv.org/abs/2403.18984
Autor:
Lang, Quanjun, Lu, Jianfeng
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 nor
Externí odkaz:
http://arxiv.org/abs/2402.11705
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 which others a
Externí odkaz:
http://arxiv.org/abs/2402.08412
Autor:
Lang, Quanjun, Lu, Fei
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 effects of
Externí odkaz:
http://arxiv.org/abs/2305.11055
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 dependence, t
Externí odkaz:
http://arxiv.org/abs/2212.14163
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
Externí odkaz:
http://arxiv.org/abs/2203.03791
Autor:
Lang, Quanjun, Lu, Fei
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 func
Externí odkaz:
http://arxiv.org/abs/2106.05565
Autor:
Lang, Quanjun, Lu, Fei
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 regularization, th
Externí odkaz:
http://arxiv.org/abs/2010.15694
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 results on
Externí odkaz:
http://arxiv.org/abs/2010.01036
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