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Framework for evaluating statistical models in physics education research

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Physical Review Physics Education Research 2021年第2期17卷 020104-020104页

作者： John M. Aiken Riccardo De Bin H. J. Lewandowski Marcos D. Caballero Center for Computing in Science Education & Department of Physics University of Oslo N-0316 Oslo Norway Department of Mathematics University of Oslo N-0316 Oslo Norway Department of Physics University of Colorado Boulder Boulder Colorado 80309 USA JILA National Institute of Standards and Technology and the University of Colorado Boulder Colorado 80309 USA Department of Physics and Astronomy Department of Computational Mathematics Sciences and Engineering and CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA

Across the field of education research there has been an increased focus on the development, critique, and evaluation of statistical methods and data usage due to recently created, very large datasets and machine learning techniques. In physics education research (PER), this increased focus has recently been shown through the 2019 Physical Review PER Focused Collection examining quantitative methods in PER. Quantitative PER has provided strong arguments for reforming courses by including interactive engagement, demonstrated that students often move away from scientistlike views due to science education, and has injected robust assessment into the physics classroom via concept inventories. The work presented here examines the impact that machine learning may have on physics education research, presents a framework for the entire process including data management, model evaluation, and results communication, and demonstrates the utility of this framework through the analysis of two types of survey data.

关键词： Research methodology

An efficient online-offline method for elliptic homogenization problems

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arXiv 2020年

作者： Huang, Yufang Ming, Pingbing Song, Siqi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We present a new numerical method for solving the elliptic homogenization problem. The main idea is that the missing effective matrix is reconstructed by solving the local least-squares in an offline stage, which shall be served as the input data for the online computation. The accuracy of the proposed method are analyzed with the aid of the refined estimates of the reconstruction operator. Two dimensional and three dimensional numerical tests confirm the efficiency of the proposed method, and illustrate that this online-offline strategy may significantly reduce the cost without loss of accuracy. Copyright © 2020, The Authors. All rights reserved.

关键词： Numerical methods

A DISCONTINUOUS GALERKIN METHOD BY PATCH RECONSTRUCTION FOR BIHARMONIC PROBLEM

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Journal of computational mathematics 2019年第4期37卷 524-540页

作者： Ruo Li Pingbing Ming Zhiyuan Sun Fanyi Yang Zhijian Yang CAPT LMAM and School of Mathematical Sciences Peking University Beijing 100871 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of Sciences No. 19A Yu-Quan Road Beijing 100049 China School of Mathematical Sciences Peking University Beijing 100871 China School of Mathematics and. Statistics Wuhan University Wuhan 430072 China

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

关键词： Least-squares problem Reconstructed basis function Discontinuous Galerkin method Biharmonic problem

Rubric-based holistic review: A promising route to equitable graduate admissions in physics

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Physical Review Physics Education Research 2022年第2期18卷 020140-020140页

作者： Nicholas T. Young K. Tollefson Remco G. T. Zegers Marcos D. Caballero Department of Physics and Astronomy Michigan State University East Lansing Michigan 48824 USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing Michigan 48824 USA National Superconducting Cyclotron Laboratory Michigan State University East Lansing Michigan 48824 USA Joint Institute for Nuclear Astrophysics Michigan State University East Lansing Michigan 48824 USA Center for Computing in Science Education and Department of Physics University of Oslo N-0316 Oslo Norway CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA

As systematic inequities in higher education and society have been brought to the forefront, graduate programs are interested in increasing the diversity of their applicants and enrollees. Yet, structures in place to evaluate applicants may not support such aims. One potential solution to support those aims is rubric-based holistic review. Starting in 2018, our physics department implemented a rubric-based holistic review process for all applicants to our graduate program. The rubric assessed applicants on 18 metrics covering their grades, test scores, research experiences, noncognitive competencies, and fit with the program. We then compared faculty’s ratings of applicants by admission status, sex, and undergraduate program over a three-year period. We find that the rubric scores show statistically significant differences between admitted and nonadmitted students as hoped. We also find that differences in rubric scores based on sex or undergraduate program reflected known systematic inequities such as applicants from smaller and less prestigious undergraduate universities scoring lower on the physics GRE and women performing more volunteer work in academia. Our results then suggest rubric-based holistic review as a possible route to making graduate admissions in physics more equitable.

关键词： Diversity & inclusion Educational policy Graduate students

A plane wave study on the localized-extended transitions in the one-dimensional incommensurate systems

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arXiv 2020年

作者： Chen, Huajie Zhou, Aihui Zhou, Yuzhi School of Mathematical Sciences Beijing Normal University Beijing100875 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Software Center for High Performance Numerical Simulation China Academy of Engineering Physics Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent experiments in the ultracold atom and photonic crystal. We formulate a propagator based scattering picture for the transition at the ground state and single particle mobility edge, in which the deeper connection between the incommensurate potentials, eigenstate compositions and transition mechanism is revealed. We further show that there exists a upper limit of localization length for all localized eigenstates, leading to an fundamental difference to the Anderson localization. Numerical calculations are presented alongside the analysis to justify our statements. The theoretical analysis and numerical methods can also be generalized to systems in higher dimensions, with different potentials or beyond the single particle regime, which would benefit the future studies in the related fields. Copyright © 2020, The Authors. All rights reserved.

关键词： Elastic waves

AN OPTIMAL PIECEWISE CUBIC NONCONFORMING FINITE ELEMENT SCHEME FOR THE PLANAR BIHARMONIC EQUATION ON GENERAL TRIANGULATIONS

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arXiv 2019年

作者： Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

This paper presents a nonconforming finite element scheme for the planar biharmonic equation which applis piecewise cubic polynomials (P3) and possesses O(h2) convergence rate in energy norm on general shape-regular triangulations. Both Dirichlet and Navier type boundary value problems are studied. The basis for the scheme is a piecewise cubic polynomial space, which can approximate the H4 functions with O(h2) accuracy in broken H2 norm. Besides, an equivalence (∇2h ·, ∇2h ·) = (∆h ·, ∆h ·), which is usually not true for nonconforming finite element spaces, is proved on the newly designed spaces. The finite element space does not correspond to a finite element defined with Ciarlet’s triple;however, a set of locally supported basis functions of the finite element space is still figured out. The notion of the finite element Stokes complex plays an important role in the analysis and also the construction of the basis functions. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

An improved gradient method with approximately optimal stepsize based on conic model for unconstrained optimization

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arXiv 2019年

作者： Liu, Zexian Liu, Hongwei State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computing AMSS Chinese Academy of Sciences Beijing1000190 China School of Mathematics and Statistics Xidian University Xi’an710126 China

A new type of stepsize, which was recently introduced by Liu and Liu (Optimization, 67(3), 427-440, 2018), is called approximately optimal stepsize and is quit efficient for gradient method. Interestingly, all gradient methods can be regarded as gradient methods with approximately optimal stepsizes. In this paper, based on the work (Numer. Algorithms 78(1), 21-39, 2018), we present an improved gradient method with approximately optimal stepsize based on conic model for unconstrained optimization. If the objective function f is not close to a quadratic on the line segment between the current and latest iterates, we construct a conic model to generate approximately optimal stepsize for gradient method if the conic model can be used;otherwise, we construct some quadratic models to generate approximately optimal stepsizes for gradient method. The convergence of the proposed method is analyzed under suitable conditions. Numerical comparisons with some well-known conjugate gradient software packages such as CG_DESCENT (SIAM J. Optim. 16(1), 170-192, 2005) and CGOPT (SIAM J. Optim. 23(1), 296-320, 2013) indicate the proposed method is very promising. Copyright © 2019, The Authors. All rights reserved.

关键词： Gradient methods

SWEMniCS: a software toolbox for modeling coastal ocean circulation, storm surges, inland, and compound flooding

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npj Natural Hazards

npj Natural Hazards 2024年第1期1卷 1-17页

作者： Clint Dawson Benjamin Pachev Jennifer Proft Eirik Valseth Mark Loveland Oden Institute for Computational Engineering and Sciences The University of Texas at Austin Austin TX USA The Department of Data Science The Norwegian University of Life Science Ås Norway Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Oslo Norway Information and Technology Laboratory Engineering Research and Development Center US Army Corps of Engineers Vicksburg MS USA

Flooding from storm surges, rainfall-runoff, and their interaction into compounding events are major natural hazards in coastal regions. To assess risks of damages to life and properties alike, numerical models are needed to guide emergency responses and future assessments. Numerical models, such as ADCIRC have over many decades shown their usefulness in such assessments. However, these models have a high threshold in terms of new user engagement as development and compilation is not trivial for users trained in compiled programming languages. Here, we develop a new open-source finite element solver for the numerical simulation of flooding. The numerical solution of the underlying PDEs is developed using the finite element framework FEniCSx. The goal is a framework where new methods can be rapidly tested before time-consuming development into codes like ADCIRC. We validate the framework on several test cases, including large-scale computations in the Gulf of Mexico for Hurricane Ike (2008).

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Evidence of large recoil velocity from a black hole merger signal

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arXiv 2022年

作者： Varma, Vijay Biscoveanu, Sylvia Islam, Tousif Shaik, Feroz H. Haster, Carl-Johan Isi, Maximiliano Farr, Will M. Field, Scott E. Vitale, Salvatore Am Mühlenberg 1 Potsdam14476 Germany LIGO Laboratory Massachusetts Institute of Technology CambridgeMA02139 United States Department of Physics Kavli Institute for Astrophysics and Space Research Massachusetts Institute of Technology 77 Massachusetts Ave CambridgeMA02139 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Center for Computational Astrophysics Flatiron Institute New YorkNY10010 United States Department of Physics and Astronomy Stony Brook University Stony Brook NY11794 United States

The final black hole left behind after a binary black hole merger can attain a recoil velocity, or a "kick", reaching values up to 5000 km/s. This phenomenon has important implications for gravitational wave astronomy, black hole formation scenarios, testing general relativity, and galaxy evolution. We consider the gravitational wave signal from the binary black hole merger GW200129_065458 (henceforth referred to as GW200129), which has been shown to exhibit strong evidence of orbital precession. Using numerical relativity surrogate models, we constrain the kick velocity of GW200129 to vf (Equation presented) km/s or vf 698 km/s (one-sided limit), at 90% credibility. This marks the first identification of a large kick velocity for an individual gravitational wave event. Given the kick velocity of GW200129, we estimate that there is a less than 0.48% (7.7%) probability that the remnant black hole after the merger would be retained by globular (nuclear star) clusters. Finally, we show that kick effects are not expected to cause biases in ringdown tests of general relativity for this event, although this may change in the future with improved detectors. © 2022, CC BY.

关键词： Merging