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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Range Geometry of Neural Operators
Published:
Research Blog
Research notes by Xiaoyang Xie on computational mathematics, scientific machine learning, and dynamical systems.
Posts
Range Geometry of Neural Operators
Published:
Three notions of dimension reveal different expressive capacities of neural operators through their range geometry.
portfolio
Portfolio item number 1
Short description of portfolio item number 1
Portfolio item number 2
Short description of portfolio item number 2
publications
Regularized Dynamic Mode Decomposition Algorithm for Time Sequence Predictions
Published in Journal 1, 2010
This paper is about the number 2. The number 3 is left for future work.
Paper Title Number 3
Published in Journal 1, 2015
This paper is about the number 3. The number 4 is left for future work.
Recommended citation: Your Name, You. (2015). "Paper Title Number 3." Journal 1. 1(3).
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Paper Title Number 4
Published in GitHub Journal of Bugs, 2024
This paper is about fixing template issue #693.
Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
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An efficient fifth-order interpolation-based Hermite WENO scheme for hyperbolic conservation laws
Published in Journal of Computational Physics, 2025
In this paper, we develop a simple, efficient, and fifth-order finite difference interpolation-based Hermite WENO (HWENO-I) scheme for one- and two-dimensional hyperbolic conservation laws. We directly interpolate the solution and first-order derivative values and evaluate the numerical fluxes based on these interpolated values. We do not need the split of the flux functions when reconstructing numerical fluxes and there is no need for any additional HWENO interpolation for the modified derivative. The HWENO interpolation only needs to be applied one time which utilizes the same candidate stencils, Hermite interpolation polynomials, and linear/nonlinear weights for the solution and first-order derivative at the cell interface, as well as the modified derivative at the cell center. The HWENO-I scheme inherits the advantages of the finite difference flux-reconstruction-based HWENO-R scheme, including fifth-order accuracy, compact stencils, arbitrary positive linear weights, and high resolution. The HWENO-I scheme is simpler and more efficient than the HWENO-R scheme and the previous finite difference interpolation-based HWENO scheme which needs the split of flux functions for the stability and upwind performance for the high-order derivative terms. Various benchmark numerical examples are presented to demonstrate the accuracy, efficiency, high resolution, and robustness of the proposed HWENO-I scheme.
talks
Talk 1 on Relevant Topic in Your Field
Published:
This is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown!
Conference Proceeding talk 3 on Relevant Topic in Your Field
Published:
This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Teaching experience 2
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.