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SSRN 2024年

作者： Kong, Lingping Velasquez, Juan D. Perfilieva, Irina Pant, Millie Pan, Jeng-Shyang Snášel, Václav Department of Computer Science VSB-Technical University of Ostrava Ostrava Czech Republic Department of Industrial Engineering University of Chile Santiago Chile Santiago Chile Institute for Research and Applications of Fuzzy Modeling Centre of Excellence IT4Innovations division of The University of Ostrava Ostrava Czech Republic Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Uttarakhand Roorkee247667 India School of Artificial Intelligence Nanjing University of Information Science and Technology China Instituto Sistemas Complejos de Ingeniería Santiago Chile Santiago Chile Faculty of Computer Science and Telecommunications Cracow University of Technology Kraków Poland Mehta Family School of Data Science and Artificial Intelligence Indian Institute of Technology Uttarakhand Roorkee247667 India College of Computer Science and Engineering Shandong University of Science and Technology China

Within the realm of data mining and machine learning, feature selection stands out as an essential technique for dimensionality reduction, presenting both popularity and complexity. Feature selection involves a nuanced trade-off that results in information loss. This distinction underscores the necessity for the development of lightweight, efficient, and practical methods capable of minimizing information loss while executing dimensional reduction. In this paper, we introduce a rankability-based feature selection method. The concept of rankability, proposed in 2019 and similar to the entropy concept, remains relatively unexplored. Our proposed method distinguishes itself by its lightweight complexity, eliminating the need for iterative *** evaluate the effectiveness of our approach, we conducted experiments on forty-one datasets and compared the results with four other algorithms using refined data with 10\%, 30\%, and 50\% feature dimension reduction. The findings reveal that our rankability-based feature selection method consistently outperforms the other four methods across a majority of datasets in terms of accuracy, precision, recall, and F1-macro performance. Specifically, the classification score exceeds 0.9 on accuracy for 50\% feature dimension reduction in twelve datasets, with nine datasets achieving scores over 0.9 in recall, F1-macro, and precision. Overall, our proposed feature selection method demonstrates promising performance. © 2024, The Authors. All rights reserved.

关键词： Feature Selection

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Time-marching based quantum solvers for time-dependent linear differential equations

arXiv

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arXiv 2022年

作者： Fang, Di Lin, Lin Tong, Yu Department of Mathematics University of California BerkeleyCA94720 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Challenge Institute for Quantum Computation University of California BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Institute for Quantum Information and Matter California Institute of Technology PasadenaCA91125 United States

The time-marching strategy, which propagates the solution from one time step to the next, is a natural strategy for solving time-dependent differential equations on classical computers, as well as for solving the Hamiltonian simulation problem on quantum computers. For more general homogeneous linear differential equations ddt|ψ(t)i = A(t)|ψ(t)i, |ψ(0)i = |ψ0i, a time-marching based quantum solver can suffer from exponentially vanishing success probability with respect to the number of time steps and is thus considered impractical. We solve this problem by repeatedly invoking a technique called the uniform singular value amplification, and the overall success probability can be lower bounded by a quantity that is independent of the number of time steps. The success probability can be further improved using a compression gadget lemma. This provides a path of designing quantum differential equation solvers that is alternative to those based on quantum linear systems algorithms (QLSA). We demonstrate the performance of the time-marching strategy with a high-order integrator based on the truncated Dyson series. The complexity of the algorithm depends linearly on the amplification ratio, which quantifies the deviation from a unitary dynamics. We prove that the linear dependence on the amplification ratio attains the query complexity lower bound and thus cannot be improved in the worst case. This algorithm also surpasses existing QLSA based solvers in three aspects: (1) A(t) does not need to be diagonalizable. (2) A(t) can be non-smooth, and is only of bounded variation. (3) It can use fewer queries to the initial state |ψ0i. Finally, we demonstrate the time-marching strategy with a first-order truncated Magnus series, which simplifies the implementation compared to high-order truncated Dyson series approach, while retaining the aforementioned benefits. Our analysis also raises some open questions concerning the differences between time-marching and QLSA based methods for

关键词： Linear systems

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Stochastic Optimisation Framework using the Core Imaging Library and Synergistic Image Reconstruction Framework for PET Reconstruction

arXiv

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arXiv 2024年

作者： Papoutsellis, Evangelos da Costa-Luis, Casper Deidda, Daniel Delplancke, Claire Duff, Margaret Fardell, Gemma Gillman, Ashley Jorgensen, Jakob S. Kereta, Zeljko Ovtchinnikov, Evgueni Pasca, Edoardo Schramm, Georg Thielemans, Kris Finden Ltd Rutherford Appleton Laboratory Harwell Campus United Kingdom Scientific Computing Department Science & Technology Facilities Council Harwell Campus United Kingdom National Physical Laboratory Electricité de France Research and Development France Australian e-Health Res. Ctr. CSIRO BrisbaneQLD Australia Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark Department of Computer Science University College London United Kingdom Department of Imaging and Pathology Division of Nuclear Medicine KU Leuven Leuven Belgium Institute of Nuclear Medicine University College London United Kingdom

We introduce a stochastic framework into the open- source Core Imaging Library (CIL) which enables easy development of stochastic algorithms. Five such algorithms from the literature are developed, Stochastic Gradient Descent, Stochastic Average Gradient (-Amélioré), (Loopless) Stochastic Variance Reduced Gradient. We showcase the functionality of the framework with a comparative study against a deterministic algorithm on a simulated 2D PET dataset, with the use of the open-source Synergistic Image Reconstruction Framework. We observe that stochastic optimisation methods can converge in fewer passes of the data than a standard deterministic algorithm1. © 2024, CC BY.

关键词： Positron emission tomography

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INTERATOMIC-POTENTIAL-FREE, DATA-DRIVEN MOLECULAR DYNAMICS

arXiv

引用

arXiv 2022年

作者： Bulin, J. Hamaekers, J. Ariza, M. Pilar Ortiz, M. Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla41092 Spain Hausdorff Center for Mathematics Universität Bonn Endenicher Allee 60 Bonn53115 Germany Division of Engineering and Applied Science California Institute of Technology 1200 E. California Blvd. PasadenaCA91125 United States

We present a Data-Driven (DD) paradigm that enables molecular dynamics calculations to be performed directly from sampled force-field data such as obtained, e. g., from ab initio calculations, thereby eschewing the conventional step of modeling the data by empirical interatomic potentials entirely. The data required by the DD solvers consists of local atomic configurations and corresponding atomic forces and is, therefore, fundamental, i. e., it is not beholden to any particular model. The resulting DD solvers, including a fully explicit DD-Verlet algorithm, are provably convergent and exhibit robust convergence with respect to the data in selected test cases. We present an example of application to C60 buckminsterfullerenes that showcases the feasibility, range and scope of the DD molecular dynamics paradigm. Copyright © 2022, The Authors. All rights reserved.

关键词： Molecular dynamics

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A Stochastic Model-Based Control Methodology for Glycemic Management in the Intensive Care Unit

arXiv

引用

arXiv 2024年

作者： Sirlanci, Melike Hripcsak, George Low Wang, Cecilia C. Stroh, J.N. Wang, Yanran Bennett, Tellen D. Stuart, Andrew M. Albers, David J. Department of Biomedical Informatics School of Medicine University of Colorado Anschutz Medical Campus AuroraCO United States Department of Applied Mathematics University of Colorado Boulder BoulderCO United States Department of Biomedical Informatics Columbia University New YorkNY United States Division of Endocrinology Metabolism and Diabetes Department of Medicine School of Medicine University of Colorado Anschutz Medical Campus AuroraCO United States Biostatiscs & Informatics Department Colorado School of Public Health AuroraCO United States Department of Computing and Mathematical Sciences California Institute of Technology PasadenaCA United States Department of Bioengineering University of Colorado Denver DenverCO United States

Intensive care unit (ICU) patients exhibit erratic blood glucose (BG) fluctuations, including hypoglycemic and hyperglycemic episodes, and require exogenous insulin delivery to keep their BG in healthy ranges. Glycemic control via glycemic management (GM) is associated with reduced mortality and morbidity in the ICU, but GM increases the cognitive load on clinicians. The availability of robust, accurate, and actionable clinical decision support (CDS) tools reduces this burden and assists in the decision-making process to improve health outcomes. Clinicians currently follow GM protocol flow charts for patient intravenous insulin delivery rate computations. We present a mechanistic model-based control algorithm that predicts the optimal intravenous insulin rate to keep BG within a target range;the goal is to develop this approach for eventual use within CDS systems. In this control framework, we employed a stochastic model representing BG dynamics in the ICU setting and used the linear quadratic Gaussian control methodology to develop a controller. We designed two experiments, one using virtual (simulated) patients and one using a real-world retrospective dataset. Using these, we evaluate the safety and efficacy of this model-based glycemic control methodology. The presented controller avoids hypoglycemia and hyperglycemia in virtual patients, maintaining BG levels in the target range more consistently than two existing GM protocols. Moreover, this methodology could theoretically prevent a large proportion of hypoglycemic and hyperglycemic events recorded in a real-world retrospective *** Codes 49-11 © 2024, CC BY-NC-ND.

关键词： Stochastic models

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The application of proximal visible and near-infrared spectroscopy to estimate soil organic matter on the Triffa Plain of Morocco

引用

International Soil and Water Conservation Research 2020年第2期8卷 195-204页

作者： Ayoub Lazaar Abdul Mounem Mouazen Kamal EL Hammouti Michael Fullen Biswajeet Pradhan Muhammad Sohail Memon Karim Andich Abdelilah Monir Laboratory of Applied Geosciences Department of GeologyFaculty of ScienceMohammed First UniversityOujdaMorocco Division of Mechatronics Biostatistics and Sensors(MeBioS)Faculty of Bioscience EngineeringKasteelpark Arenberg 30B-3001 HeverleeBelgium Faculty of Science and Engineering University of WolverhamptonWolverhamptonWV11LYUnited Kingdom Center for Advanced Modelling and Geospatial Information Systems(CAMGIS) Faculty of Engineering and Information TechnologyUniversity of Technology SydneySydney2007NSWAustralia Faculty of Agricultural Engineering Sindh Agriculture UniversityTandojam70060Pakistan Laboratory of Applied Geomatics and Soil Science National Institute of Agronomic Research(INRA)OujdaMorocco Department of Mathematics EDP and Scientific Computing TeamMoulay Ismail UniversityMéknesMorocco

Soil organic matter (SOM) is a fundamental soil constituent. The estimation of this parameter in the laboratory using the classical method is complex time-consuming and requires the use of chemical re-agents. The objectives of this study were to assess the accuracy of two laboratory measurement setups of the VIS-NIR spectroscopy in estimating SOM content and determine the important spectral bands in the SOM estimation model. A total of 115 soil samples were collected from the non-root zone (0-20 cm) of soil in the study area of the Triffa Plain and then analysed for SOM in the laboratory by the Walkley-Black method. The reflectance spectra of soil samples were measured by two protocols, Contact Probe (CP) and Pistol Grip (PG)) of the ASD spectroradiometer (350-2500 nm) in the laboratory. Partial least squares regression (PLSR) was used to develop the prediction models. The results of coefficient of determination (R2) and the root mean square error (RMSE) showed that the pistol grip offers reasonable accuracy with an R2=0.93 and RMSE=0.13 compared to the contact probe protocol with an R2=0.85 and RMSE = 0.19. The near-Infrared range were more accurate than those in the visible range for pre-dicting SOM using the both setups (CP and PG). The significant wavelengths contributing to the pre-diction of SOM for (PG) setup were at:424, 597, 1432, 1484, 1830,1920, 2200, 2357 and 2430 nm, while were at 433, 587, 1380, 1431, 1929, 2200 and 2345 nm for (CP) setup.

关键词： Soil organic matter VIS-NIR spectroscopy Reflectance spectra SOM estimation SOM analysis

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Progress on Feynman Integrals for 2 → 3 scattering at NNLO 38

Progress on Feynman Integrals for 2 → 3 scattering at NNLO

引用

38th Conference on Recent Developments in High Energy Physics and Cosmology, HEP 2021

作者： Canko, D.D. Kardos, A. Papadopoulos, C.G. Smirnov, A.V. Syrrakos, N. Wever, C. Institute of Nuclear and Particle Physics NCSR ‘Demokritos’ Agia Paraskevi15310 Greece Department of Physics University of Athens Zographou15784 Greece Physics Division National Technical University of Athens Athens15780 Greece University of Debrecen Faculty of Science and Technology Department of Experimental Physics PO Box 105 Debrecen4010 Hungary Research Computing Center Moscow State University Moscow119991 Russia Moscow Center for Fundamental and Applied Mathematics Moscow119992 Russia Physik-Department T31 Technische Universitat Munchen James-Franck Strasse 1 GarchingD-85748 Germany

We present recent results on two-loop five-point Feynman Integrals with one off-shell leg that are relevant to the study of many 2 → 3 scattering processes of interest at the LHC, especially for the leading-colour W + 2 jets production. The calculation is based on the Simplified Differential Equations approach. © 2021 Institute of Physics Publishing. All rights reserved.

关键词： Differential equations

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Leveraging randomized compiling for the quantum imaginary-time-evolution algorithm

引用

Physical Review Research 2022年第3期4卷 033140-033140页

作者： Jean-Loup Ville Alexis Morvan Akel Hashim Ravi K. Naik Marie Lu Bradley Mitchell John-Mark Kreikebaum Kevin P. O'Brien Joel J. Wallman Ian Hincks Joseph Emerson Ethan Smith Ed Younis Costin Iancu David I. Santiago Irfan Siddiqi Quantum Nanoelectronics Laboratory Dept. of Physics University of California at Berkeley Berkeley California 94720 USA Computational Research Division Lawrence Berkeley National Lab Berkeley California 94720 USA Materials Sciences Division Lawrence Berkeley National Lab Berkeley California 94720 USA Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Inst. for Quantum Computing and Dept. of Applied Mathematics University of Waterloo Waterloo Ontario Canada N2L 3G1 Quantum Benchmark Inc. Kitchener Ontario Canada N2H 5G5

Recent progress in noisy intermediate-scale quantum (NISQ) hardware shows that quantum devices may be able to tackle complex problems even without error correction. However, coherent errors due to the increased complexity of these devices is an outstanding issue. They can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like quantum imaginary time evolution are susceptible to these errors. This article presents the combination of both noise tailoring using randomized compiling and error mitigation with purification. We also show that cycle benchmarking gives an estimate of the reliability of the purification. We apply this method to the quantum imaginary time evolution of a transverse field Ising model and report an energy estimation error and a ground-state infidelity both below 1%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices.

关键词： Measurement-based quantum computing Quantum algorithms Quantum benchmarking Quantum computation Quantum control Quantum information processing Quantum simulation

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Solving inverse stochastic problems from discrete particle observations using the fokker-planck equation and physics-informed neural networks

arXiv

引用

arXiv 2020年

作者： Chen, Xiaoli Yang, Liu Duan, Jinqiao Karniadakis, George Em Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan430074 China Division of Applied Mathematics Brown University ProvidenceRI02912 United States Department of Applied Mathematics College of Computing Illinois Institute of Technology ChicagoIL60616 United States Pacific Northwest National Laboratory RichlandWA99354 United States

The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants, hence requiring the development of a data-driven modeling approach. When the data available is directly on the PDF, then there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles’ positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback-Leibler divergence to connect the stochastic samples with the FP equation, to simultaneously learn the equation and infer the multi-dimensional PDF at all times. In particular, we consider two types of inverse problems, type I where the FP equation is known but the initial PDF is unknown, and type II in which, in addition to unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. We demonstrate the new PINN framework in detail in the one-dimensional case (1D) but we also provide results for up to 5D demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles. Copyright © 2020, The Authors. All rights reserved.

关键词： Deep neural networks

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Democratizing Uncertainty Quantification

arXiv

引用

arXiv 2024年

作者： Seelinger, Linus Reinarz, Anne Lykkegaard, Mikkel B. Akers, Robert Alghamdi, Amal M.A. Aristoff, David Bangerth, Wolfgang Bénézech, Jean Diez, Matteo Frey, Kurt Jakeman, John D. Jørgensen, Jakob S. Kim, Ki-Tae Kent, Benjamin M. Martinelli, Massimiliano Parno, Matthew Pellegrini, Riccardo Petra, Noemi Riis, Nicolai A.B. Rosenfeld, Katherine Serani, Andrea Tamellini, Lorenzo Villa, Umberto Dodwell, Tim J. Scheichl, Robert Scientific Computing Center Karlsruhe Institute of Technology Karlsruhe Germany Department of Computer Science Durham University Durham United Kingdom digiLab Exeter United Kingdom UK Atomic Energy Authority Oxford United Kingdom Lyngby Denmark Department of Mathematics Colorado State University Fort CollinsCO United States Department of Mathematics Department of Geosciences Colorado State University Fort CollinsCO United States Centre for Integrated Materials Processes and Structures Department of Mechanical Engineering University of Bath Bath United Kingdom National Research Council Institute of Marine Engineering Rome Italy Institute for Disease Modeling Global Health Division Bill & Melinda Gates Foundation United States Optimization and Uncertainty Quantification Sandia National Laboratories AlbuquerqueNM United States University of California Merced United States National Research Council-Institute for Applied Mathematics and Information Technologies "E. Magenes" Pavia Italy Solea Energy ThetfordVT United States Copenhagen Imaging ApS Herlev Denmark The University of Texas Austin United States Heidelberg University Germany

Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance computing (HPC) scale. In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support. © 2024, CC BY-NC-ND.

关键词： Application programs

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