128 citations · 513 across the 59 of their papers we have counts for
7 papers · 1 filter
Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs
Nathaniel Trask, Andy Huang, Xiaozhe Hu
As traditional machine learning tools are increasingly applied to science and engineering applications, physics-informed methods have emerged as effective tools for endowing infere…
A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations
James H. Adler, Casey Cavanaugh, Xiaozhe Hu +1
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of t…
A Posteriori Error Estimates for Solving Graph Laplacians
Xiaozhe Hu, Kaiyi Wu, Ludmil T. Zikatanov
In this paper, we study a posteriori error estimators which aid multilevel iterative solvers for linear systems with graph Laplacians. In earlier works such estimates were computed…
Randomized Fast Subspace Descent Methods
Long Chen, Xiaozhe Hu, Huiwen Wu
Randomized Fast Subspace Descent (RFASD) Methods are developed and analyzed for smooth and non-constraint convex optimization problems. The efficiency of the method relies on a spa…
Rejuvenating AMLI-Cycle: From Chebyshev Polynomials to Momentum Acceleration
Chunyan Niu, Yunhui He, Xiaozhe Hu
In this paper, we investigate the AMLI-cycle method and make two contributions. First, we revisit the AMLI-cycle using the Chebyshev polynomials and establish a theory for its unif…
Modeling, well-posedness and discretization for a class of models for mixed-dimensional problems with high dimensional gap
Erlend Hodneland, Xiaozhe Hu, Jan Martin Nordbotten
In this work, we illustrate the underlying mathematical structure of mixed-dimensional models arising from the composition of graphs and continuous domains. Such models are becomin…
Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and Applications to Biological Networks
Lenore Cowen, Kapil Devkota, Xiaozhe Hu +2
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffus…