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MATRIX-FREE GPU-ACCELERATED SADDLE-POINT SOLVERS FOR HIGH-ORDER PROBLEMS IN H(div)

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arXiv 2023年

作者： Pazner, Will Kolev, Tzanio Vassilevski, Panayot Fariborz Maseeh Department of Mathematics and Statistics Portland State University PortlandOR United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA United States

This work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in H(div). The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis (cf. SIAM J. Sci. Comput., 45 (2023), A675–A702), efficient matrix-free preconditioners can be constructed for the (1, 1)-block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian, and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the "crooked pipe" grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case. Copyright © 2023, The Authors. All rights reserved.

关键词： Porous materials

Recommender System to Identify Drug-Target Associations Using Matrix Factorization

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Recommender System to Identify Drug-Target Associations Usin...

International ECTI Northern Section Conference on Electrical, Electronics, Computer and Telecommunications Engineering (ECTI-NCON)

作者： Sornsawan Phuangmalai Apichat Suratanee Kitiporn Plaimas Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok Thailand Department of Mathematics Faculty of Applied Science and Intelligent and Nonlinear Dynamic Innovations Research Center King Mongkut’s University of Technology North Bangkok Bangkok Thailand Department of Mathematics and Computer Science Advance Virtual and Intelligent Computing (AVIC) Center Faculty of Science Chulalongkorn University Bangkok Thailand

Recommender systems, widely used in information filtering systems, demonstrate efficacy in suggesting novel items to users. In this study, we propose the application of a recommender system to predict new drug-target associations. Here, drugs are represented as users, while protein targets are treated as items within the recommender system. However, due to sparse data in a matrix of drugs and protein targets, matrix factorization (MF) techniques are employed to decompose the extensive matrix into smaller matrices. We identify non-negative matrix factorization (NMF) and singular value decomposition (SVD) as top-performing models for this task. Subsequently, we integrated them into the traditional recommender system, encompassing both drug-based collaborative filtering and target-based collaborative filtering, to identify new drug-target associations aligned with observed interactions between drugs and target proteins. Finally, we evaluated the performance of our developed recommender system with matrix factorization for drug-target associations and compared the results with those obtained from a recommender system without matrix factorization.

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A tumor-immune model of chronic myeloid leukemia with optimal immunotherapeutic protocols

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arXiv 2025年

作者： Zhang, Haifeng Zhuge, Changjing Lei, Jinzhi School of Mathematical Sciences Jiangsu University Zhenjiang212013 China Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing100124 China School of Mathematical Sciences Center for Applied Mathematics Tiangong University Tianjin300387 China

The interactions between tumor cells and the immune system play a crucial role in cancer evolution. In this study, we explore how these interactions influence cancer progression by modeling the relationships among naive T cells, effector T cells, and chronic myeloid leukemia cells. We examine the existence of equilibria, the asymptotic stability of the positive steady state, and the global stability of the tumor-free equilibrium. Additionally, we develop a partial differential equation to describe the conditions under which the concentration of cancer cells reaches a level that allows for effective control of cancer evolution. Finally, we apply our proposed model to investigate optimal treatment strategies that aim to minimize both the concentration of cancer cells at the end of treatment and the accumulation of tumor burden, as well as the cost associated with treatment during the intervention period. Our study reveals an optimal therapeutic protocol using optimal control theory. We perform numerical simulations to illustrate our theoretical results and to explore the dynamic behavior of the system and optimal therapeutic protocols. The simulations indicate that the optimal treatment strategy can be more effective than a constant treatment approach, even when applying the same treatment interval and total drug input. Copyright © 2025, The Authors. All rights reserved.

关键词： T-cells

Enhanced prairie dog optimization with Levy flight and dynamic opposition-based learning for global optimization and engineering design problems

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Neural computing and Applications 2024年第19期36卷 11137-11170页

作者： Biswas, Saptadeep Shaikh, Azharuddin Ezugwu, Absalom El-Shamir Greeff, Japie Mirjalili, Seyedali Bera, Uttam Kumar Abualigah, Laith Department of Mathematics National Institute of Technology Agartala Tripura Agartala India Unit for Data Science and Computing North-West University 11 Hoffman Street Potchefstroom2520 South Africa Faculty of Natural and Agricultural Sciences School of Computer Science and Information Systems North-West University Vanderbijlpark South Africa Centre for Artificial Intelligence Research and Optimization Torrens University Australia Fortitude Valley BrisbaneQLD4006 Australia Research Center University of Tabuk Tabuk71491 Saudi Arabia Computer Science Department Al al-Bayt University Mafraq25113 Jordan Hourani Center for Applied Scientific Research Al-Ahliyya Amman University Amman19328 Jordan Applied Science Research Center Applied Science Private University Amman11931 Jordan Department of Electrical and Computer Engineering Lebanese American University Byblos13-5053 Lebanon School of Engineering and Technology Sunway University Malaysia Petaling Jaya27500 Malaysia College of Engineering Yuan Ze University Taoyuan32003 Taiwan MEU Research Unit Middle East University Amman11831 Jordan

This study proposes a new prairie dog optimization algorithm version called EPDO. This new version aims to address the issues of premature convergence and slow convergence that were observed in the original PDO algorithm. To improve performance, several modifications are introduced in EPDO. First, a dynamic opposite learning strategy is employed to increase the diversity of the population and prevent premature convergence. This strategy helps the algorithm avoid falling into local optima and promotes global optimization. Additionally, the Lévy dynamic random walk technique is utilized in EPDO. This modified Lévy flight with random walk reduces the algorithm’s running time for the test function’s ideal value, accelerating its convergence. The proposed approach is evaluated using 33 benchmark problems from CEC 2017 and compared against seven other comparative techniques: GWO, MFO, ALO, WOA, DA, SCA, and RSA. Numerical results demonstrate that EPDO produces good outcomes and performs well in solving benchmark problems. To further validate the results and assess reliability, the authors employ average rank tests, the measurement of alternatives, and ranking according to the compromise solution (MARCOS) method, as well as a convergence report of EPDO and other algorithms. Furthermore, the effectiveness of the EPDO algorithm is demonstrated by applying it to five design problems. The results indicate that EPDO achieves impressive outcomes and proves its capability to address practical issues. The algorithm performs well in solving benchmark and practical design problems, as supported by the numerical results and validation methods used in the study. © The Author(s) 2024.

关键词： Global optimization

Towards Graph Neural Network Surrogates Leveraging Mechanistic Expert Knowledge for Pandemic Response

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arXiv 2024年

作者： Schmidt, Agatha Zunker, Henrik Heinlein, Alexander Kühn, Martin J. Institute of Software Technology Department of High-Performance Computing German Aerospace Center Cologne Germany Delft Institute of Applied Mathematics Delft University of Technology Netherlands Life and Medical Sciences Institute University of Bonn Bonn Germany

MSC Codes 68T07, 92B20, 92B05During the COVID-19 crisis, mechanistic models have been proven fundamental to guide evidence-based decision making. However, time-critical decisions in a dynamically changing environment restrict the time available for modelers to gather supporting evidence. As infectious disease dynamics are often heterogeneous on a spatial or demographic scale, models should be resolved accordingly. In addition, with a large number of potential interventions, all scenarios can barely be computed on time, even when using supercomputing facilities. We suggest to combine complex mechanistic models with data-driven surrogate models to allow for on-the-fly model adaptations by public health experts. We build upon a spatially and demographically resolved infectious disease model and train a graph neural network for data sets representing early phases of the pandemic;cf Fig. 3. The resulting networks reached an execution time of less than a second, a significant speedup compared to the metapopulation approach. The suggested approach yields potential for on-the-fly execution and, thus, integration of disease dynamics models in low-barrier website applications. For the approach to be used with decision-making, datasets with larger variance will have to be considered. Copyright © 2024, The Authors. All rights reserved.

关键词： Graph neural networks

Understanding Comparative Genomics Data Visualization for Biodiversity Domain Through Persona-Based Interviews

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Understanding Comparative Genomics Data Visualization for Bi...

2024 IEEE International Conference on computing, ICOCO 2024

作者： Chan, Vei Siang Mohamed, Farhan Bin Salleh, Faezah Binti Mohd Iglesias, Andres Jamaludin, Najwa Ayuni Binti Mustafa Albakri, Ikmal Faiq Albakri Media and Game Innovation Center of Excellence Institute of Human Centered Engineering Universiti Teknologi Malaysia Johor Bahru Malaysia Department of Biosciences Faculty of Science Universiti Teknologi Malaysia Johor Bahru Malaysia Department of Applied Mathematics and Computational Sciences Universidad de Cantabria Santander Spain Pervasive Computing & Educational Technology Department of Media Interactive Fakulti Teknologi Maklumat dan Komunikasi Universiti Teknikal Malaysia Melaka Melaka Malaysia

ISBN: (纸本)9798331530303

Understanding the needs of genomic data visualization techniques is important to help bioinformaticians to perform their comparative analytical tasks effectively. DNA sequencing datasets consist of a long sequential string of nucleotide base pairs combination and are often involved in multiple sequences alignment for comparative analysis. Therefore, existing challenges include designing suitable visualization layout and the need of user-centered approach to ensure optimal user experience. Existing works also featured heavily on the qualitative evaluation of comparative visualization tools, such as use cases and case studies, which are difficult to quantify and conduct follow up evaluation for tool improvement. Hence, this paper aims to understand the needs of visualization tools in comparative genomic analysis to identify visualization tasks and visual design requirements. The methodology includes the creation of semi-structured interview based on personas template as guiding questions and the synthesis of thematic analysis results. These results presented the requirements of the visualization tasks for the biodiversity domain based on comparative targets. For future work, this research will design, develop, and validate the comparative visualization tool based on the discovered requirements. ©2024 IEEE.

关键词： Genome

Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning

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arXiv 2024年

作者： Chang, Tyler Gillette, Andrew Maulik, Romit Mathematics and Computer Science Division Argonne National Laboratory United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Information Sciences and Technology Department The Pennsylvania State University United States

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. In this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently;(2) comparative performance among distinct interpolants can aid in validation goals;(3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository. © 2024, CC BY-NC-SA.

关键词： Interpolation

Fast θ -Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis

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Computational and applied mathematics 2023年第3期42卷

作者： Wang, Mengjie Dai, Xinjie Yu, Yanyan Xiao, Aiguo Hunan Key Laboratory for Computation and Simulation in Science and Engineering National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Yunnan University Yunnan Kunming650504 China

In this paper, a fast θ-Maruyama method is proposed for solving stochastic Volterra integral equations of convolution type with singular and Hölder continuous kernels based on the sum-of-exponentials approximation. Furthermore, the average storage O(N) and the calculation cost O(N2) of θ-Maruyama scheme are reduced to O(log N) and O(Nlog N) for T 1 or O(log 2N) and O(Nlog 2N) for T≈ 1 , respectively, which implies that the fast θ-Maruyama scheme is confirmed to improve the computational efficiency of the θ-Maruyama method. Under the local Lipschitz and linear growth conditions, strong convergence of the given numerical scheme are obtained. Then, for the linear test equation, we show the asymptotic behavior of solutions in mean square sense. Further, we obtain the explicit structure of the stability matrices and some numerical results of the mean-square stability for the fast θ-Maruyama method applied to the linear test equation. Finally, some numerical experiments are also given to illustrate the effectiveness of the method. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

关键词： Computational efficiency

A posteriori error estimation for an interior penalty virtual element method of Kirchhoff plates

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arXiv 2024年

作者： Feng, Fang Hu, Yuming Yu, Yue Zhao, Jikun School of Mathematics and Statistics Nanjing University of Science and Technology Nanjing China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Zhengzhou University Zhengzhou450001 China

In this paper, we develop a residual-type a posteriori error estimation for an interior penalty virtual element method (IPVEM) for the Kirchhoff plate bending problem. Building on the work in [18], we adopt a modified discrete variational formulation that incorporates the H1-elliptic projector in the jump and average terms. This allows us to simplify the numerical implementation by including the H1-elliptic projector in the computable error estimators. We derive the reliability and efficiency of the a posteriori error bound by constructing an enriching operator and establishing some related error estimates that align with C0-continuous interior penalty finite element methods. As observed in the a priori analysis, the interior penalty virtual elements exhibit similar behaviors to C0continuous elements despite its discontinuity. This observation extends to the a posteriori estimate since we do not need to account for the jumps of the function itself in the discrete scheme and the error estimators. As an outcome of the error estimator, an adaptive VEM is introduced by means of the mesh refinement strategy with the one-hanging-node rule. Numerical results from several benchmark tests confirm the robustness of the proposed error estimators and show the efficiency of the resulting adaptive VEM. Copyright © 2024, The Authors. All rights reserved.

关键词： Discrete element methods