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AN EFFICIENT SPECTRAL TRUST-REGION DEFLATION METHOD FOR MULTIPLE SOLUTIONS

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arXiv 2023年

作者： Li, Lin Wang, Li-Lian Li, Huiyuan School of Mathematics and Physics Hunan Key Laboratory for Mathematical Modeling and Scientific Computing University of South China Hengyang421001 China Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University 637371 Singapore State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China

It is quite common that a nonlinear partial differential equation (PDE) admits multiple distinct solutions and each solution may carry a unique physical meaning. One typical approach for finding multiple solutions is to use the Newton method with different initial guesses that ideally fall into the basins of attraction confining the solutions. In this paper, we propose a fast and accurate numerical method for multiple solutions comprised of three ingredients: (i) a well-designed spectral-Galerkin discretization of the underlying PDE leading to a nonlinear algebraic system (NLAS) with multiple solutions;(ii) an effective deflation technique to eliminate a known (founded) solution from the other unknown solutions leading to deflated NLAS;and (iii) a viable nonlinear least-squares and trust-region (LSTR) method for solving the NLAS and the deflated NLAS to find the multiple solutions sequentially one by one. We demonstrate through ample examples of differential equations and comparison with relevant existing approaches that the spectral LSTR-Deflation method has the merits: (i) it is quite flexible in choosing initial values, even starting from the same initial guess for finding all multiple solutions;(ii) it guarantees high-order accuracy;and (iii) it is quite fast to locate multiple distinct solutions and explore new solutions which are not reported in literature. Copyright © 2023, The Authors. All rights reserved.

关键词： Newton-Raphson method

Eliminating Order Reduction on Linear, Time-Dependent ODEs with GARK Methods

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arXiv 2022年

作者： Roberts, Steven Sandu, Adrian Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA United States Computational Science Laboratory Department of Computer Science Virginia Tech 2202 Kraft Dr. BlacksburgVA24060 United States

When applied to stiff, linear differential equations with time-dependent forcing, Runge-Kutta methods can exhibit convergence rates lower than predicted by the classical order condition theory. Commonly, this order reduction phenomenon is addressed by using an expensive, fully implicit Runge-Kutta method with high stage order or a specialized scheme satisfying additional order conditions. This work develops a flexible approach of augmenting an arbitrary Runge-Kutta method with a fully implicit method used to treat the forcing such as to maintain the classical order of the base scheme. Our methods and analyses are based on the general-structure additive Runge-Kutta framework. Numerical experiments using diagonally implicit, fully implicit, and even explicit Runge-Kutta methods confirm that the new approach eliminates order reduction for the class of problems under consideration, and the base methods achieve their theoretical orders of *** Codes 65L04, 65L20 Copyright © 2022, The Authors. All rights reserved.

关键词： Runge Kutta methods

Enhanced multiple sclerosis diagnosis by MRI image retrieval using convolutional autoencoders

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Egyptian Informatics Journal 2025年 30卷

作者： Haggag, R.M. Ali, Eman M. Khalifa, M.E. Taha, Mohamed Scientific Computing Department Faculty of Computers and Artificial Intelligence Benha University Egypt Scientific Computing Department Faculty of Computer and Information Sciences Ain Shams University Egypt Computer Science Department Faculty of Computers and Artificial Intelligence Benha University Egypt

Multiple sclerosis (MS) is an autoimmune disorder characterized by damage to the central nervous system (CNS), leading to neuronal degeneration and affecting over 2.8 million individuals globally. Early and accurate diagnosis of MS is critical, given its significant social and economic consequences. Magnetic resonance imaging (MRI) remains the gold standard for MS diagnosis and monitoring. This study introduces a novel Content-Based Medical Image Retrieval (CBMIR) framework that leverages a newly designed Convolutional Autoencoder (CAE) model to improve the diagnostic evaluation of MS-related MRI scans. The proposed system extracts latent features from query and reference MRI images using the CAE. Extensive ablation studies involving nine distance metrics and diverse feature space dimensions identify 64 as the optimal latent feature size and validate the Mahalanobis distance as the superior similarity measure. Evaluated on four publicly available MS MRI datasets, the framework achieves Mean Average Precision (MAP) scores of 91.23%, 98.68%, 99.88%, and 99.69%, respectively, demonstrating enhanced diagnostic accuracy. The system also outperforms existing similar CBMIR frameworks for other diseases in MAP scores and generalizes effectively without requiring extensive preprocessing or segmentation. The primary contribution of this work is the development of a CAE-driven CBMIR system optimized for MS diagnosis, achieving state-of-the-art MAP performance while maintaining an average retrieval latency of 780 ms outperforming the compared systems. © 2025

关键词： Content based retrieval

computing Truncated Joint Approximate Eigenbases for Model Order Reduction

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arXiv 2022年

作者： Loring, Terry Vides, Fredy Department of Mathematics and Statistics University of New Mexico Albuquerque United States Scientific Computing Innovation Center School of Mathematics and Computer Science Universidad Nacional Autónoma de Honduras Tegucigalpa Honduras

In this document, some elements of the theory and algorithmics corresponding to the existence and computability of approximate joint eigenpairs for finite collections of matrices with applications to model order reduction, are presented. More specifically, given a finite collection $X_1,\ldots,X_d$ of Hermitian matrices in $\mathbb{C}^{n\times n}$, a positive integer $r\ll n$, and a collection of complex numbers $\hat{x}_{j,k}\in \mathbb{C}$ for $1\leq j\leq d$, $1\leq k\leq r$. First, we study the computability of a set of $r$ vectors $w_1,\ldots,w_r\in \mathbb{C}^{n}$, such that $w_k=\arg\min_{w\in \mathbb{C}^n}\sum_{j=1}^d\|X_jw-\hat{x}_{j,k} w\|^2$ for each $1\leq k \leq r$, then we present a model order reduction procedure based on the truncated joint approximate eigenbases computed with the aforementioned techniques. Some prototypical algorithms together with some numerical examples are presented as well. Copyright © 2022, The Authors. All rights reserved.

关键词： Matrix algebra

The Case for Non-Volatile RAM in Cloud HPCaaS

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arXiv 2022年

作者： Fridman, Yehonatan Harel, Re'em Oren, Gal Department of Computer Science Ben-Gurion University of the Negev Israel Israel Atomic Energy Commission Scientific Computing Center Nuclear Research Center Negev Israel Department of Physics Nuclear Research Center Negev Israel Department of Computer Science Technion Israel Institute of Technology Israel

HPC as a service (HPCaaS) is a new way to expose HPC resources via cloud services. However, continued effort to port large-scale tightly coupled applications with high interprocessor communication to multiple (and many) nodes synchronously, as in on-premise supercomputers, is still far from satisfactory due to network latencies. As a consequence, in said cases, HPCaaS is recommended to be used with one or few instances. In this paper we take the claim that new piece of memory hardware, namely Non-Volatile RAM (NVRAM), can allow such computations to scale up to an order of magnitude with marginalized penalty in comparison to RAM. Moreover, we suggest that the introduction of NVRAM to HPCaaS can be cost-effective to the users and the suppliers in numerous forms. © 2022, CC BY.

关键词： Random access storage

Evidence-Aware Multi-Modal Data Fusion and its Application to Total Knee Replacement Prediction

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Evidence-Aware Multi-Modal Data Fusion and its Application t...

Proceedings of the Digital Image computing: Technqiues and Applications (DICTA)

作者： Xinwen Liu Jing Wang S. Kevin Zhou Craig Engstrom Shekhar S. Chandra School of Electrical Engineering and Computer Science The University of Queensland Brisbane Australia The Commonwealth Scientific and Industrial Research Organisation Canberra Australia Center for Medical Imaging Robotics Analytic Computing & Learning (MIRACLE) School of Biomedical Engineering & Suzhou Institute for Advanced Research University of Science and Technology of China Suzhou China Key Laboratory of Intelligent Information Processing of Chinese Academy of Sciences (CAS) Institute of Computing Technology CAS Beijing China School of Human Movement and Nutrition Sciences The University of Queensland Brisbane Australia

ISBN: (数字)9798350379037

ISBN: (纸本)9798350379044

Deep neural networks have been widely studied to predict a medical condition, such as total knee replacement (TKR). It has shown that data of different modalities, such as imaging data, clinical variables, and demographic information, provide complementary information and thus can improve the prediction accuracy together. However, the data sources of various modalities may not always be of high quality, and each modality may have only partial information of medical condition. Thus, predictions from different modalities can be in conflict, and the final prediction may fail in the presence of such a conflict. Therefore, it is important to account for the reliability of each source data and the prediction output when making a final decision. In this paper, we propose an evidence-aware multimodal data fusion framework based on the Dempster-Shafer theory (DST). The backbone models contain an image branch, a non-image branch and a fusion branch. For each branch, there is an evidence network that takes the extracted features as input and outputs an evidence score, which is designed to represent the reliability of the output from the current branch. The output probabilities along with the evidence scores from multiple branches are combined with the Dempster's combination rule to make a final prediction. Experimental results on the public OA initiative (OAI) dataset for the TKR prediction task show that the proposed method has better performance by accounting for conflicts from various modalities.

关键词： Medical conditions Soft sensors Digital images Data integration Imaging Artificial neural networks Reliability theory Feature extraction Reliability engineering Knee replacement

A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics

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A Scalable Real-Time Data Assimilation Framework for Predict...

High Performance computing, Networking, Storage and Analysis, SC-W: Workshops of the International Conference for

作者： Junqi Yin Siming Liang Siyan Liu Feng Bao Hristo G. Chipilski Dan Lu Guannan Zhang National Center for Computational Science Oak Ridge National Laboratory Oak Ridge TN USA Department of Mathematics Florida State University Tallahassee FL USA Computational Science and Engineering Division Oak Ridge National Laboratory Oak Ridge TN USA Department of Scientific Computing Florida State University Tallahassee FL USA Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge TN USA

ISBN: (数字)9798350355543

ISBN: (纸本)9798350355550

AI-based foundation models like FourCastNet, GraphCast, ClimaX, and Pangu-Weather are revolutionizing weather and climate predictions but are not yet ready for operational use. Their limitation lies in the absence of a data assimilation system to incorporate real-time Earth system observations, crucial for accurately forecasting events like tropical cyclones and atmospheric rivers. To overcome these obstacles, we introduce a generic real-time data assimilation framework and demonstrate its end-to-end performance on the Frontier supercomputer. This framework comprises two primary modules: an ensemble score filter (EnSF), which significantly outperforms the state-of-the-art data assimilation method, e.g., the Local Ensemble Transform Kalman Filter (LETKF); and a vision transformer-based surrogate capable of real-time adaptation through the integration of observational data. We demonstrate both the strong and weak scaling of our framework up to 1024 GPUs on the Exascale supercomputer, Frontier. Our results not only illustrate the framework’s exceptional scalability on high-performance computing systems, but also demonstrate the importance of supercomputers in real-time data assimilation for weather and climate predictions. Even though the proposed framework is tested only on a benchmark surface quasi-geostrophic (SQG) turbulence system, it has the potential to be combined with existing AI-based foundation models, making it suitable for future operational implementations.

关键词： Earth Foundation models Computational modeling High performance computing Scalability Atmospheric modeling Supercomputers Real-time systems Numerical models Data assimilation

Clustering-Based Model Reduction for Glioma Graph Networks

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Clustering-Based Model Reduction for Glioma Graph Networks

Medical Imaging 2025: Clinical and Biomedical Imaging

作者： Mlinarić, P. Sokolikj, Z. Talla, G. Meyer-Baese, U. Stadlbauer, A. Malberg, H. Na, C.-H. Juetten, K. Wiestler, B. Meyer-Baese, A. Department of Mathematics Virginia Tech United States Department of Scientific Computing Florida State University TallahasseeFL United States Department of Electrical and Computer Engineering FAMU-FSU College of Engineering TallahasseeFL United States Department of Neurosurgery Friedrich-Alexander University of Erlangen-Nürnberg Germany Institute for Biomedical Engineering Technical University of Dresden Germany Aachen Germany Departments of Neuroradiology & Radiation Oncology TUM School of Medicine Health Technical University of Munich Germany Institute for Advanced Study Technical University of Munich Germany Department of Neurosurgery RWTH Aachen University Aachen52074 Germany Department of Computer Science Florida State University TallahasseeFL United States

ISBN: (纸本)9781510685987

We analyze structural and functional connectivity graphs for both healthy and glioma subjects by clustering-based model reduction to obtain a detailed understanding of these complex graphs. The reduced-order network is obtained by dividing the connected brain regions or nodes into disjoint clusters. Further, each cluster is replaced by a single new node in a reduced-size graph network. Several partitions are analyzed and evaluated based on model reduction errors. © 2025 SPIE.

关键词： Bayesian networks

Generalizing Reduction-Based Algebraic Multigrid

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arXiv 2022年

作者： Zaman, Tareq Nytko, Nicolas Taghibakhshi, Ali MacLachlan, Scott Olson, Luke West, Matthew Interdisciplinary Program in Scientific Computing Memorial University of Newfoundland NL Canada Department of Computer Science University of Illinois at Urbana-Champaign IL United States Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign IL United States

Algebraic Multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their performance. Reduction-based AMG (AMGr) algorithms attempt to formalize these heuristics by providing two-level convergence bounds that depend concretely on properties of the partitioning of the given matrix into its fine- and coarse-grid degrees of freedom. MacLachlan and Saad (SISC 2007) proved that the AMGr method yields provably robust two-level convergence for symmetric and positive-definite matrices that are diagonally dominant, with a convergence factor bounded as a function of a coarsening parameter. However, when applying AMGr algorithms to matrices that are not diagonally dominant, not only do the convergence factor bounds not hold, but measured performance is notably degraded. Here, we present modifications to the classical AMGr algorithm that improve its performance on matrices that are not diagonally dominant, making use of strength of connection, sparse approximate inverse (SPAI) techniques, and interpolation truncation and rescaling, to improve robustness while maintaining control of the algorithmic costs. We present numerical results demonstrating the robustness of this approach for both classical isotropic diffusion problems and for non-diagonally dominant systems coming from anisotropic diffusion. Copyright © 2022, The Authors. All rights reserved.

关键词： Matrix algebra