arXiv subjects

Chen Miao

Publications and source records attributed to Chen Miao.

3 recordsLinked to original sources

arXiv2026

Comparative study of different quadrature methods for cut elements

The quadrature of cut elements is crucial for all Finite Element Methods that do not apply boundary-fitted meshes. It should be efficient, accurate, and robust. Various approaches balancing these requirements have been published, with some available as open-source implementations. This work reviews these open-sources codes and the methods used. Furthermore, benchmarking examples are developed for 2D and 3D geometries. Implicit and explicit boundary descriptions are available for all models. The different examples test the efficiency, accuracy, versatility, and robustness of the codes. Special focus is set on the influence of the input parameter, which controls the desired quadrature order, on the actual integration error. A detailed comparison of the discussed codes is carried out. The benchmarking allows a conclusive comparison and presents a valuable tool for future code development. All tests are published in an accompanying open-source repository.

cs.CE↗

arXiv2025

Employing Continuous Integration inspired workflows for benchmarking of scientific software -- a use case on numerical cut cell quadrature

In the field of scientific computing, one often finds several alternative software packages (with open or closed source code) for solving a specific problem. These packages sometimes even use alternative methodological approaches, e.g., different numerical discretizations. If one decides to use one of these packages, it is often not clear which one is the best choice. To make an informed decision, it is necessary to measure the performance of the alternative software packages for a suitable set of test problems, i.e. to set up a benchmark. However, setting up benchmarks ad-hoc can become overwhelming as the parameter space expands rapidly. Very often, the design of the benchmark is also not fully set at the start of some project. For instance, adding new libraries, adapting metrics, or introducing new benchmark cases during the project can significantly increase complexity and necessitate laborious re-evaluation of previous results. This paper presents a proven approach that utilizes established Continuous Integration tools and practices to achieve high automation of benchmark execution and reporting. Our use case is the numerical integration (quadrature) on arbitrary domains, which are bounded by implicitly or parametrically defined curves or surfaces in 2D or 3D.

cs.SE↗

arXiv2020

Eigen component analysis: A quantum theory incorporated machine learning technique to find linearly maximum separable components

For a linear system, the response to a stimulus is often superposed by its responses to other decomposed stimuli. In quantum mechanics, a state is the superposition of multiple eigenstates. Here, by taking advantage of the phase difference, a common feature as we identified in data sets, we propose eigen component analysis (ECA), an interpretable linear learning model that incorporates the principle of quantum mechanics into the design of algorithm design for feature extraction, classification, dictionary and deep learning, and adversarial generation, etc. The simulation of ECA, possessing a measurable $class\text{-}label$ $\mathcal{H}$, on a classical computer outperforms the existing classical linear models. Eigen component analysis network (ECAN), a network of concatenated ECA models, enhances ECA and gains the potential to be not only integrated with nonlinear models, but also an interface for deep neural networks to implement on a quantum computer, by analogizing a data set as recordings of quantum states. Therefore, ECA and ECAN promise to expand the feasibility of linear learning models, by adopting the strategy of quantum machine learning to replace heavy nonlinear models with succinct linear operations in tackling complexity.

cs.LG↗