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arXiv 2020年

作者： Guo, Ling Narayan, Akil Liu, Yongle Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT United States Department of Mathematics Southern University of Science and Technology Shenzhen China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

One of the open problems in the field of forward uncertainty quantification (UQ) is the ability to form accurate assessments of uncertainty having only incomplete information about the distribution of random inputs. Another challenge is to efficiently make use of limited training data for UQ predictions of complex engineering problems, particularly with high dimensional random parameters. We address these challenges by combining data-driven polynomial chaos expansions with a recently developed preconditioned sparse approximation approach for UQ problems. The first task in this two-step process is to employ the procedure developed in (Ahlfeld et al. 2016, [1]) to construct an "arbitrary" polynomial chaos expansion basis using a finite number of statistical moments of the random inputs. The second step is a novel procedure to effect sparse approximation via 1 minimization in order to quantify the forward uncertainty. To enhance the performance of the preconditioned 1 minimization problem, we sample from the so-called induced distribution, instead of using Monte Carlo (MC) sampling from the original, unknown probability measure. We demonstrate on test problems that induced sampling is a competitive and often better choice compared with sampling from asymptotically optimal measures (such as the equilibrium measure) when we have incomplete information about the distribution. We demonstrate the capacity of the proposed induced sampling algorithm via sparse representation with limited data on test functions, and on a Kirchoff plating bending problem with random Young’s modulus. Copyright © 2020, The Authors. All rights reserved.

关键词： Probability distributions

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OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle

arXiv

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arXiv 2020年

作者： Yu, Haijun Tian, Xinyuan Weinan, E. Li, Qianxiao NCMIS 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 Department of Mathematics The Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics National University of Singapore Singapore119077 Singapore Institute of High Performance Computing A*STAR Singapore138632 Singapore

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parameterized by neural networks that retain clear physical structure information, such as free energy, diffusion, conservative motion and external forces. For high dimensional problems with a low dimensional slow manifold, an autoencoder with metric preserving regularization is introduced to find the low dimensional generalized coordinates on which we learn the generalized Onsager dynamics. Our method exhibits clear advantages over existing methods on benchmark problems for learning ordinary differential equations. We further apply this method to study Rayleigh-Bénard convection and learn Lorenz-like low dimensional autonomous reduced order models that capture both qualitative and quantitative properties of the underlying dynamics. This forms a general approach to building reduced order models for forced dissipative *** Codes 76E30, 34D20, 68T05/07, 82C35 Copyright © 2020, The Authors. All rights reserved.

关键词： Ordinary differential equations

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Complexity Analysis and Algorithm Design of Pooling Problem

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Journal of the Operations Research Society of China 2018年第2期6卷 249-266页

作者： Yu-Hong Dai Rui Diao Kai Fu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The pooling problem,also called the blending problem,is fundamental in production planning of *** can be formulated as an optimization problem similar with the minimum-cost flow ***,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general *** also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of *** this paper,we prove that the pooling problem is still strongly NP-hard even with only one *** means the quality is an essential difference between minimum-cost flow problem and the pooling *** solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming *** convergence of the algorithm is *** numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local *** results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.

关键词： Pooling problem Complexity analysis Successive linear programming Non-monotone

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PRACTICAL NEWTON METHODS FOR ELECTRONIC STRUCTURE CALCULATIONS ∗

arXiv

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arXiv 2020年

作者： Dai, Xiaoying Zhang, Liwei Zhou, Aihui 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

In this paper, we propose and analyze some practical Newton methods for electronic structure calculations. We show the convergence and the local quadratic convergence rate for the Newton method when the Newton search directions are well-obtained. In particular, we investigate some basic implementation issues in determining the search directions and step sizes which ensures the convergence of the subproblem at each iteration and accelerates the algorithm, respectively. It is shown by our numerical experiments that our Newton methods perform better than the existing conjugate gradient method, and the Newton method with the adaptive step size strategy is even more efficient. Copyright © 2020, The Authors. All rights reserved.

关键词： Newton-Raphson method

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Automatic Diagnosis of Myocarditis Disease in Cardiac MRI Modality using Deep Transformers and Explainable Artificial Intelligence

arXiv

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arXiv 2022年

作者： Jafari, Mahboobeh Shoeibi, Afshin Ghassemi, Navid Heras, Jonathan Ling, Sai Ho Beheshti, Amin Zhang, Yu-Dong Wang, Shui-Hua Alizadehsani, Roohallah Gorriz, Juan M. Acharya, U. Rajendra Rokny, Hamid Alinejad Internship in BioMedical Machine Learning Lab The Graduate School of Biomedical Engineering UNSW Sydney SydneyNSW2052 Australia Data Science and Computational Intelligence Institute University of Granada Spain Department of Mathematics and Computer Science University of La Rioja La Rioja Spain Australia Data Analytics Lab Department of Computing Macquarie University SydneyNSW2109 Australia School of Computing and Mathematical Sciences University of Leicester Leicester United Kingdom Deakin University VIC3217 Australia Department of Psychiatry University of Cambridge United Kingdom School of Mathematics Physics and Computing University of Southern Queensland Springfield Australia BioMedical Machine Learning Lab The Graduate School of Biomedical Engineering UNSW Sydney SydneyNSW2052 Australia UNSW Data Science Hub The University of New South Wales SydneyNSW2052 Australia Research Centre Macquarie University Sydney2109 Australia

Myocarditis is a significant cardiovascular disease (CVD) that poses a threat to the health of many individuals by causing damage to the myocardium. The occurrence of microbes and viruses, including the likes of HIV, plays a crucial role in the development of myocarditis disease (MCD). The images produced during cardiac magnetic resonance imaging (CMRI) scans are low contrast, which can make it challenging to diagnose cardiovascular diseases. In other hand, checking numerous CMRI slices for each CVD patient can be a challenging task for medical doctors. To overcome the existing challenges, researchers have suggested the use of artificial intelligence (AI)-based computer-aided diagnosis systems (CADS). The presented paper outlines a CADS for the detection of MCD from CMR images, utilizing deep learning (DL) methods. The proposed CADS consists of several steps, including dataset, preprocessing, feature extraction, classification, and post-processing. First, the Z-Alizadeh dataset was selected for the experiments. Subsequently, the CMR images underwent various preprocessing steps, including denoising, resizing, as well as data augmentation (DA) via CutMix and MixUp techniques. In the following, the most current deep pre-trained and transformer models are used for feature extraction and classification on the CMR images. The findings of our study reveal that transformer models exhibit superior performance in detecting MCD as opposed to pre-trained architectures. In terms of DL architectures, the Turbulence Neural Transformer (TNT) model exhibited impressive accuracy, reaching 99.73% utilizing a 10-fold cross-validation approach. Additionally, to pinpoint areas of suspicion for MCD in CMRI images, the Explainable-based Grad Cam method was employed. © 2022, CC BY-NC-ND.

关键词： Diseases

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Algebraic multigrid block preconditioning for multi-group radiation diffusion equations

arXiv

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arXiv 2020年

作者： Yue, Xiaoqiang Zhang, Shulei Xu, Xiaowen Shu, Shi Shi, Weidong School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Xiangtan411105 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Applied Mathematics Shanxi University of Finance and Economics Taiyuan030006 China

The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume discretization of multi-group radiation diffusion equations, whose coefficient matrices can be rearranged into the (G + 2) × (G + 2) block form, where G is the number of energy groups. The preconditioning techniques are based on the monolithic classical algebraic multigrid method, physical-variable based coarsening two-level algorithm and two types of block Schur complement preconditioners. The classical algebraic multigrid is applied to solve the subsystems that arise in the last three block preconditioners. The coupling strength and diagonal dominance are further explored to improve performance. We use representative one-group and twenty-group linear systems from capsule implosion simulations to test the robustness, efficiency, strong and weak parallel scaling properties of the proposed methods. Numerical results demonstrate that block preconditioners lead to mesh- and problem-independent convergence, and scale well both algorithmically and in parallel. Copyright © 2020, The Authors. All rights reserved.

关键词： Finite volume method

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Physics Graduate Record Exam does not help applicants “stand out”

引用

Physical Review Physics Education Research 2021年第1期17卷 010144-010144页

作者： Nicholas T. Young 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 Center for Computing in Science Education & Department of Physics University of Oslo N-0316 Oslo Norway CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA

One argument for keeping the physics Graduate Record Exam (GRE) is that it can help applicants who might otherwise be missed in the admissions process stand out. In this work, we evaluate whether this claim is supported by physics graduate school admissions decisions. We used admissions data from five Ph.D.-granting physics departments over a 2-year period (N=2537) to see how the fraction of applicants admitted varied based on their physics GRE scores. We compared applicants with low GPAs to applicants with higher GPAs, applicants from large undergraduate universities to applicants from smaller undergraduate universities, and applicants from selective undergraduate institutions to applicants from less selective undergraduate institutions. We also performed a mediation and moderation analysis to provide statistical rigor and to better understand the previous relationships. We find that for applicants who might otherwise have been missed (e.g., have a low GPA or attended a small or less selective school), having a high physics GRE score did not seem to increase the applicant’s chances of being admitted to the schools. However, having a low physics GRE score seemed to penalize otherwise competitive applicants (i.e., applicants with mid to high GPAs). Thus, our work suggests that the physics GRE does not, in fact, help applicants who might otherwise be missed stand out.

关键词： Diversity & inclusion Educational policy Graduate students

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Validating the predictions of mathematical models describing tumor growth and treatment response

arXiv

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arXiv 2025年

作者： Lorenzo, Guillermo Hormuth, David A. Wu, Chengyue Pash, Graham Chaudhuri, Anirban Lima, Ernesto A.B.F. Okereke, Lois C. Patel, Reshmi Willcox, Karen Yankeelov, Thomas E. Group of Numerical Methods in Engineering Department of Mathematics University of A Coruña Spain Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX United States Livestrong Cancer Institutes The University of Texas at Austin AustinTX United States Department of Imaging Physics The University of Texas MD Anderson Cancer Center HoustonTX United States Department of Breast Imaging The University of Texas MD Anderson Cancer Center HoustonTX United States Department of Biostatistics The University of Texas MD Anderson Cancer Center HoustonTX United States Institute for Data Science in Oncology The University of Texas MD Anderson Cancer Center HoustonTX United States Texas Advanced Computing Center The University of Texas at Austin AustinTX United States Department of Biomedical Engineering The University of Texas at Austin AustinTX United States Department of Diagnostic Medicine The University of Texas at Austin AustinTX United States Department of Oncology The University of Texas at Austin AustinTX United States

Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer mechanisms and personalize disease management. To address these limitations, individualized cancer forecasts have been shown to predict tumor growth and therapeutic response, inform treatment optimization, and guide experimental efforts. These predictions are obtained via computer simulations of mathematical models that are constrained with data from a patient’s cancer and experiments. This book chapter addresses the validation of these mathematical models to forecast tumor growth and treatment response. We start with an overview of mathematical modeling frameworks, model selection techniques, and fundamental metrics. We then describe the usual strategies employed to validate cancer forecasts in preclinical and clinical scenarios. Finally, we discuss existing barriers in validating these predictions along with potential strategies to address them. © 2025, CC BY-NC-ND.

关键词： Prediction models

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Developing a learning goal framework for computational thinking in computationally integrated physics classrooms

arXiv

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arXiv 2021年

作者： Weller, Daniel P. Bott, Theodore E. Caballero, Marcos D. Irving, Paul W. Department of Physics & Astronomy Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science & Engineering CREATE for STEM Institute Michigan State University East LansingMI48824 United States Department of Physics Center for Computing in Science Education University of Oslo Oslo0316 Norway

computational thinking has been a recent focus of education research within the sciences. However, there is a dearth of scholarly literature on how best to teach and to assess this topic, especially in disciplinary science courses. Physics classes with computation integrated into the curriculum are a fitting setting for investigating computational thinking. In this paper, we lay the foundation for exploring computational thinking in introductory physics courses. First, we review relevant literature to synthesize a set of potential learning goals that students could engage in when working with computation. The computational thinking framework that we have developed features 14 practices contained within 6 different categories. We use in-class video data as existence proofs of the computational thinking practices proposed in our framework. In doing this work, we hope to provide ways for teachers to assess their students’ development of computational thinking, while also giving physics education researchers some guidance on how to study this topic in greater depth. Copyright © 2021, The Authors. All rights reserved.

关键词： Curricula

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Data-driven surrogate modeling of seismic uplift capacity for strip anchors in frictional–cohesive soils with surcharge using isogeometric analysis

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Ocean engineering 2025年 336卷

作者： Nguyen-Minh, Toan Bui-Ngoc, Tram Shiau, Jim Nguyen, Tan Nguyen-Thoi, Trung Faculty of Civil Engineering Ton Duc Thang University Ho Chi Minh City Viet Nam Laboratory for Computational Mechanics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City Viet Nam Faculty of Mechanical - Electrical and Computer Engineering School of Technology Van Lang University Ho Chi Minh City Viet Nam School of Engineering University of Southern Queensland Toowoomba 4350 QLD Australia Smart Computing in Civil Engineering Research Group Faculty of Civil Engineering Ton Duc Thang University Ho Chi Minh City Viet Nam Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City Viet Nam

The behavior of strip anchors under uplift loads in complex conditions, such as frictional–cohesive soils with surcharge and seismic loading, poses significant engineering challenges. This study presents a data-driven surrogate modeling framework to predict seismic uplift capacity, combining high-fidelity simulations with machine learning. A large dataset is generated using Upper Bound Limit Analysis (UBLA) implemented via Isogeometric Analysis (IGA) and Second-Order Cone Programming (SOCP). Key input variables i.e., cohesion factor (c'/γB), internal friction angle (φ′), embedment ratio (H/B), seismic coefficients (Kh, Kv), and surcharge factor (q/γB), are evaluated to explore their impact on uplift capacity (Pu/γB). Sensitivity analysis highlights embedment ratio and internal friction angle as major factors enhancing uplift, while seismic coefficients reduce it, especially in low-cohesion soils. The Levenberg-Marquardt Neural Network (LMNN) outperforms other machine learning models, achieving a mean squared error (MSE) of 0.006 ± 0.000 on training and 0.005 ± 0.001 on testing data, with an R² of 1.000. This integration of IGA-UB with LMNN provides reliable upper-bound estimates for uplift capacity, particularly in high-cohesion soils. The development of a closed-form solution ensures practical relevance, making this hybrid approach a powerful tool for engineering design under varied loading scenarios.

关键词： Closed-form solution Frictional-cohesive soils Isogeometric analysis Machine learning Sensitivity analysis Strip anchors Uplift capacity

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