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arXiv 2022年

作者： Schauer, Lucas Schmidt, Michael J. Engdahl, Nicholas B. Pankavich, Stephen D. Benson, David A. Bolster, Diogo Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM87185 United States Department of Civil and Environmental Engineering Washington State University PullmanWA99164 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States Department of Civil and Environmental Engineering and Earth Sciences University of Notre Dame Notre Dame IN46556 United States

We develop a multi-dimensional, parallelized domain decomposition strategy (DDC) for mass-transfer particle tracking (MTPT) methods. These methods are a type of Lagrangian algorithm for simulating reactive transport and are able to be parallelized by employing large numbers of CPU cores to accelerate run times. In this work, we investigate different procedures for "tiling" the domain in two and three dimensions, (2-d and 3-d), as this type of formal DDC construction is currently limited to 1-d. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-d for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-d parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run up to around 2700 cores, reducing a 5-hour simulation to 8 seconds, and the 3-d algorithm maintains appreciable speedup up to 1700 cores. Copyright © 2022, The Authors. All rights reserved.

关键词： Lagrange multipliers

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End-to-end quantum machine learning implemented with controlled quantum dynamics

arXiv

引用

arXiv 2020年

作者： Wu, Re-Bing Cao, Xi Xie, Pinchen Liu, Yu-Xi Department of Automation Tsinghua University Beijing100084 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Micro-Nano Electronics Tsinghua University Beijing100084 China

This work presents a hardware-friendly end-to-end quantum machine learning scheme that can be implemented with imperfect near-term intermediate-scale quantum processors. The proposal transforms the machine learning task to the optimization of a quantum control system, which parameterize the learning model by experimentally tunable control variables. Our design also enables automated feature selection by encoding the raw input data to quantum states through agent control variables. Comparing with the gate-based parameterized quantum circuits, the resulting end-to-end quantum learning models is easy to implement as there are only few ad-hoc parameters to be determined by the designer. Numerical simulations on the benchmarking MNIST dataset without down-sampling the images demonstrate that the proposed scheme can achieve comparable high performance with only 3-5 qubits than known quantum machine learning models. The scheme is promising for efficiently performing large-scale real-world learning tasks using intermediate-scale quantum processors. Copyright © 2020, The Authors. All rights reserved.

关键词： Benchmarking

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Digital Audio Watermarking by Amplitude Embedding System 15th

Digital Audio Watermarking by Amplitude Embedding System

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15th International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIH-MSP 2019, held in conjunction with the 12th International Conference on Frontiers of Information Technology, Applications and Tools, FITAT 2019

作者： Lin, Meng-Ju Zhao, Ming Chen, Shuo-Tsung Chen, Ching-Ju Department of Applied Mathematics Tunghai University No. 1727 Sec.4 Taiwan Boulevard Taichung Taiwan40704 Taiwan School of Computer Science Yangtze University Jingzhou CityHubei Province China College of Future Bachelor Program in Interdisciplinary Studies National Yunlin University of Science and Technology TaiwanYunlin64002 Taiwan National Yunlin University of Science and Technology TaiwanYunlin64002 Taiwan

ISBN: (纸本)9789811397134

This paper proposed an amplitude embedding system for digital audio watermarking in the wavelet domain. In this paper, the relationship between the watermarked coefficients and the original coefficients is first presented and then amplitude-based embedding rules are combined into an amplitude-based embedding system that incorporates a system state. For the embedding in this system, the information includes synchronization codes and the watermarks are embedded into the DWT lowest frequency sub-band coefficients which can be described by a matrix form. Moreover, the SNR is rewritten as a performance index which is a quadratic form. Then, a nonlinear function connecting the performance index and the embedding system is derived. Accordingly, an optimization-based embedding system is proposed. Finally, the Karush–Kuhn–Tucker (KKT) Theorem is used to obtain the optimal solution, which is an important formula for watermarking. In addition, the hidden information can be extracted without knowledge of the original audio. In the experiments, the performance of the proposed system is tested and the results verify the high SNR and strong robustness against multimedia signal processing or malicious attacks. © 2020, Springer Nature Singapore Pte Ltd.

关键词： Embeddings

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Uncertainty quantification by random measures and fields

arXiv

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arXiv 2020年

作者： Bastian, Caleb Deen Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Massive Dynamics PrincetonNJ08542 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk functionals of input-output maps. These are the ANOVA decomposition of the intensity measure and the decomposition of the random measure variance, each into subspaces. Orthogonal random measures furnish sensitivity distributions. We show that the random counting measure may be used to construct positive random fields, which admit decompositions of covariance and sensitivity indices and may be used to represent interacting particle systems. The first and second order global sensitivity analyses conveyed through random counting measures elucidate and integrate different notions of uncertainty quantification, and the global sensitivity analysis of random fields conveys the proportionate functional contributions to covariance. This framework complements others when used in conjunction with for instance algorithmic uncertainty and model selection uncertainty *** Codes 60G57, 60G60, 60G55 © 2020, CC-BY-NC-ND.

关键词： Uncertainty analysis

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Learning equations from biological data with limited time samples

arXiv

引用

arXiv 2020年

作者： Nardini, John T. Lagergren, John H. Hawkins-Daarud, Andrea Curtin, Lee Morris, Bethan Rutter, Erica M. Swanson, Kristin R. Flores, Kevin B. Department of Mathematics North Carolina State University RaleighNC United States Statistical and Applied Mathematical Sciences Insitute DurhamNC United States Mathematical NeuroOncology Laboratory Precision Neurotherapeutics Innovation Program Mayo Clinic PhoenixAZ United States Centre for Mathematical Medicine and Biology University of Nottingham Nottingham United Kingdom Department of Applied Mathematics University of California Merced MercedCA United States

Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets, however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data is sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions. Copyright © 2020, The Authors. All rights reserved.

关键词： Learning systems

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Relationship between eddies and SSH in the Indian Ocean during April 2020

引用

AIP Conference Proceedings 2024年第1期3082卷

作者： M. N. Hidayat R. Wafdan M. Ikhwan M. Ramli Z. A. Muchlisin S. Sugianto M. A. Chaliluddin Samsul Rizal Mathematics Graduate Study Program Universitas Syiah Kuala Banda Aceh 23111 Indonesia Graduate School of Mathematics and Applied Sciences Universitas Syiah Kuala Banda Aceh 23111 Indonesia Department of Marine Sciences Faculty of Marine and Fisheries Universitas Syiah Kuala Banda Aceh 23111 Indonesia Department of Mathematics Universitas Syiah Kuala Banda Aceh 23111 Indonesia Department of Aquaculture Faculty of Marine and Fisheries Universitas Syiah Kuala Banda Aceh 23111 Indonesia Research Center for Marine Sciences and Fisheries Universitas Syiah Kuala Banda Aceh 23111 Indonesia Department of Soil Sciences Faculty of Agriculture Universitas Syiah Kuala Banda Aceh 23111 Indonesia Department of Fisheries Resource Utilization Faculty of Marine and Fisheries Universitas Syiah Kuala Banda Aceh 23111 Indonesia

Eddies occur almost everywhere in the oceans and play an important role in ocean circulation. They represent a large part of the ocean’s kinetic energy and may indicate their transport and mixing of temperature and salinity. This study investigates the relationship between eddies, sea surface height (SSH), and sea surface temperature (SST) in the Indian Ocean in April 2020. We carry out the analysis using monthly average data for currents, SSH, and SST from the data portal Copernicus Marine Environment Monitoring Service (CMEMS) together with wind data from the National Centers for Environmental Prediction (NCEP) / National Center for Atmospheric Research (NCAR) for April 2020. From the results of this study, we found that two eddies occurred in Aceh waters (coordinates (93°E,5°N) and (98°E,6°N)) in the northern hemisphere. The two Eddies occur with minimal SSH contours in the middle. The direction of the eddies appears in the form of a current counterclockwise movement. Because it occurs in the Northern Hemisphere, the current movement is deflected to the right, resulting in upwelling. The occurrence of a cold SST in the middle of the eddies confirms the appearance of the two eddies.

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Using Cluster Analysis and Dynamic programming for Demand Response applied to Electricity Load in Residential Homes

引用

Journal of Engineering for Sustainable Buildings and Cities 2020年第1期1卷 011006页

作者： Chanpiwat, Pattanun Gabriel, Steven A. Moglen, Rachel L. Siemann, Michael J. Department of Mechanical Engineering University of Maryland College Park 20742 MD United States Department of Mechanical Engineering and the Applied Mathematics Statistics and Scientific Computation Program University of Maryland College Park 20742 MD United States Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Trondheim NO-7491 Norway Operations Research and Industrial Engineering The University of Texas at Austin Austin 78712 TX United States Resideo Technologies Austin 78702 TX United States

This paper develops means to analyze and cluster residential households into homogeneous groups based on the electricity load. Classifying customers by electricity load profiles is a top priority for retail electric providers (REPs), so they can plan and conduct demand response (DR) effectively. We present a practical method to identify the most DR-profitable customer groups as opposed to tailoring DR programs for each separate household, which may be computationally prohibitive. Electricity load data of 10,000 residential households from 2017 located in Texas was used. The study proposed the clustered load-profile method (CLPM) to classify residential customers based on their electricity load profiles in combination with a dynamic program for DR scheduling to optimize DR profits. The main conclusions are that the proposed approach has an average 2.3% profitability improvement over a business-as-usual heuristic. In addition, the proposed method on average is approximately 70 times faster than running the DR dynamic programming separately for each household. Thus, our method not only is an important application to provide computational business insights for REPs and other power market participants but also enhances resilience for power grid with an advanced DR scheduling tool. Copyright © 2020 by ASME.

关键词： cluster analysis customer classification demand response dynamic programming energy efficiency integrated systems occupant behavior optimization residential household

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A deep learning-based ODE solver for chemical kinetics

arXiv

引用

arXiv 2020年

作者： Zhang, Tianhan Zhang, Yaoyu Weinan, E. Ju, Yiguang Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Qing Yuan Research Institute Shanghai Jiao Tong University Shanghai200240 China Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Developing efficient and accurate algorithms for chemistry integration is a challenging task due to its strong stiffness and high dimensionality. The current work presents a deep learning-based numerical method called DeepCombustion0.0 to solve stiff ordinary differential equation systems. The homogeneous autoignition of DME/air mixture, including 54 species, is adopted as an example to illustrate the validity and accuracy of the algorithm. The training and testing datasets cover a wide range of temperature, pressure, and mixture conditions between 750 – 1200 K, 30 – 50 atm, and equivalence ratio = 0.7 – 1.5. Both the first-stage low-temperature ignition (LTI) and the second-stage high-temperature ignition (HTI) are considered. The methodology highlights the importance of the adaptive data sampling techniques, power transform preprocessing, and binary deep neural network (DNN) design. By using the adaptive random samplings and appropriate power transforms, smooth submanifolds in the state vector phase space are observed, on which two three-layer DNNs can be appropriately trained. The neural networks are end-to-end, which predict temporal gradients of the state vectors directly. The results show that temporal evolutions predicted by DNN agree well with traditional numerical methods in all state vector dimensions, including temperature, pressure, and species concentrations. Besides, the ignition delay time differences are within 1%. At the same time, the CPU time is reduced by more than 20 times and 200 times compared with the HMTS and VODE method, respectively. The current work demonstrates the enormous potential of applying the deep learning algorithm in chemical kinetics and combustion modeling. © 2020, CC BY.

关键词： Numerical methods

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Manifestations of metastable criticality in the long-range structure of model water glasses

arXiv

引用

arXiv 2021年

作者： Gartner, Thomas E. Torquato, Salvatore Car, Roberto Debenedetti, Pablo G. Department of Chemistry Princeton University PrincetonNJ United States Department of Physics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ United States

Much attention has been devoted to water’s metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship between these phenomena remains incompletely understood. Using molecular dynamics simulations of the realistic TIP4P/2005 model, we found a striking signature of the liquid-liquid critical point in the structure of water glasses, manifested as a pronounced increase in long-range density fluctuations at pressures proximate to the critical pressure. By contrast, these signatures were absent in glasses of two model systems that lack a critical point. We also characterized the departure from equilibrium upon vitrification via the non-equilibrium index;water-like systems exhibited a strong pressure dependence in this metric, whereas simple liquids did not. These results reflect a surprising relationship between the metastable equilibrium phenomenon of liquid-liquid criticality and the non-equilibrium structure of glassy water, with implications for our understanding of water phase behavior and glass physics. Our calculations suggest a possible experimental route to probing the existence of the liquid-liquid transition in water and other fluids. © 2021, CC BY.

关键词： Criticality (nuclear fission)

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Evolving Fuzzy System applied to Battery Charge Capacity Prediction for Fault Prognostics

arXiv

引用

arXiv 2021年

作者： Camargos, Murilo Osorio Bessa, Iury Cordovil Junior, Luiz A.Q. Silva Coutinho, Pedro Henrique Leite, Daniel Furtado Palhares, Reinaldo Martínez School of Applied Mathematics Fundação Getulio Vargas Rio de Janeiro Brazil Graduate Program in Electrical Engineering Federal University of Minas Gerais Belo Horizonte Brazil Department of Electricity Federal University of Amazonas Manaus Brazil Department of Automatics Federal University of Lavras Lavras Brazil Department of Electronics Engineering Federal University of Minas Gerais Belo Horizonte Brazil

This paper addresses the use of data-driven evolving techniques applied to fault prognostics. In such problems, accurate predictions of multiple steps ahead are essential for the Remaining Useful Life (RUL) estimation of a given asset. The fault prognostics’ solutions must be able to model the typical nonlinear behavior of the degradation processes of these assets, and be adaptable to each unit’s particularities. In this context, the Evolving Fuzzy Systems (EFSs) are models capable of representing such behaviors, in addition of being able to deal with non-stationary behavior, also present in these problems. Moreover, a methodology to recursively track the model’s estimation error is presented as a way to quantify uncertainties that are propagated in the long-term predictions. The well-established NASA’s Li-ion batteries data set is used to evaluate the models. The experiments indicate that generic EFSs can take advantage of both historical and stream data to estimate the RUL and its uncertainty. © 2021, CC BY-NC-SA.

关键词： NASA

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