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

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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

Adaptive tikhonov strategies for stochastic ensemble Kalman inversion

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arXiv 2021年

作者： Weissmann, Simon Chada, Neil K. Schillings, Claudia Tong, Xin T. Interdisciplinary Center for Scientific Computing University of Heidelberg Heidelberg69120 Germany Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal KSA 23955 Saudi Arabia Mannheim School of Computer Science and Mathematics University of Mannheim Mannheim68131 Germany Department of Mathematics National University of Singapore Singapore119077 Singapore

Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov strategies for EKI. This work builds upon Tikhonov EKI (TEKI) which was proposed for a fixed regularization constant. By adaptively learning the regularization parameter, this procedure is known to improve the recovery of the underlying unknown. For the analysis, we consider a continuous-time setting where we extend known results such as well-posdeness and convergence of various loss functions, but with the addition of noisy observations. Furthermore, we allow a time-varying noise and regularization covariance in our presented convergence result which mimic adaptive regularization schemes. In turn we present three adaptive regularization schemes, which are highlighted from both the deterministic and Bayesian approaches for inverse problems, which include bilevel optimization, the MAP formulation and covariance learning. We numerically test these schemes and the theory on linear and nonlinear partial differential equations, where they outperform the non-adaptive TEKI and *** Codes 65M32, 60G35, 65C35, 70F17 Copyright © 2021, The Authors. All rights reserved.

关键词： Continuous time systems

$H(\mathrm {div})$ preconditioning for a mixed finite element formulation of the diffusion problem with random data

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mathematics of Computation 2010年第270期79卷 733-760页

作者： Elman, Howard Furnival, Darran Powell, Catherine Department of Computer Science and Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 Applied Mathematics and Scientific Computing Program University of Maryland College Park Maryland 20742 National Oceanographic Centre Southampton S014 32H School of Mathematics University of Manchester Oxford Road Manchester M13 9PL United Kingdom

Abstract: We study $H(\mathrm {div})$ preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for an $H(\mathrm {div})$ operator with random weight function acting on a certain tensor product space of random fields with finite variance. We build on the Arnold-Falk-Winther multigrid algorithm presented in 1997 by varying the spatial discretization from grid to grid whilst keeping the stochastic discretization fixed. We extend the deterministic analysis to accommodate the modified $H(\mathrm {div})$ operator and establish spectral equivalence bounds with a new multigrid V-cycle operator that are independent of the spatial and stochastic discretization parameters. We implement multigrid within a block-diagonal preconditioner for the full saddle-point problem, derive eigenvalue bounds for the preconditioned system matrices and investigate the impact of all the discretization parameters on the convergence rate of preconditioned minres.

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Modeling subgrid-scale force and divergence of heat flux of compressible isotropic turbulence by artificial neural network

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Physical Review Fluids 2019年第10期4卷 104605-104605页

作者： Chenyue Xie Ke Li Chao Ma Jianchun Wang Shenzhen Key Laboratory of Complex Aerospace Flows Center for Complex Flows and Soft Matter Research Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China Institute of Computational Mathematics and Scientific Engineering Computing Chinese Academy of Sciences Beijing 100190 People's Republic of China The Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In this paper, the subgrid-scale (SGS) force and the divergence of SGS heat flux of compressible isotropic turbulence are modeled directly by an artificial neural network (ANN), which serves as a data-driven SGS modeling tool for large-eddy simulations (LESs). The unclosed SGS force and divergence of SGS heat flux are modeled based on the local stencil geometry with Galilean invariance. The input features include the first-order and second-order derivatives of filtered velocity and temperature, filtered density, and its first-order derivative. It is shown that the proposed ANN-F7 model shows an advantage over the gradient model in the a priori test. Specifically, the ANN-F7 model gives larger correlation coefficients and smaller relative errors than the gradient model. In an a posteriori analysis, the ANN-F7 model performs better than the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM) in the prediction of the statistical properties of flow fields at the Taylor microscale Reynolds number Reλ ranging from 180 to 250. The DSM and DMM models lead to the typical tilted spectral distribution of velocity, where low wave numbers are too energy rich, while those near the cutoff are damped too strongly. In contrast, it is shown that the velocity spectrum predicted by the ANN-F7 model almost overlaps with the filtered direct numerical simulation data. Besides, the ANN-F7 model reconstructs the probability density functions of SGS force and divergence of SGS heat flux much better than the DSM and DMM models. An artificial neural network with reasonable physical input features can deepen our understanding of turbulence modeling.

关键词： Compressible flows Turbulence Artificial neural networks

A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

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arXiv 2023年

作者： Herrala, Olli Gabriel, Steven A. Oliveira, Fabricio Ekholm, Tommi Aalto University Department of Mathematics and Systems Analysis Espoo Finland University of Maryland Department of Mechanical Engineering/Applied Mathematics Statistics & Scientific Computing Program College ParkMD United States Norwegian University of Science and Technology Department of Industrial Economics and Technology Management Trondheim Norway Finnish Meteorological Institute Helsinki Finland

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed methods, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio. Copyright © 2023, The Authors. All rights reserved.

关键词： Energy resources

A Simulation-Based Model for Optimal Demand Response Load Shifting: A Case Study for the Texas Power Market

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SSRN

SSRN 2019年

作者： Schaperow, Jacob R. Gabriel, Steven A. Siemann, Michael Crawford, Jaden Civil and Environmental Engineering University of California Los Angeles 420 Westwood Plaza 6722 Boelter Hall Los AngelesCA90095 United States Mechanical Engineering/Applied Mathematics Statistics & Scientific Computing Program University of Maryland College ParkMD20742 United States Whisker Labs 12410 Milestone Center Drive GermantownMD20876 United States

This paper describes a prototype Monte Carlo simulation tool that we use to evaluate retail demand response (DR) programs for the Texas power market (the Electric Reliability Council of Texas/ERCOT), but which could also be applied to other regions. The model simulates a direct load control technique in which customers’ power consumption is adjusted during certain time periods called DR events. During a DR event, smart thermostats automatically increase participating customers’ temperature setpoints, reducing air-conditioning loads and thus potentially shielding retail electric providers (REPs) from financial losses during times of peak load. This study identified a Pareto optimal load control schedule based on forecasted load, settlement point prices and weather variables, taking into account stochastic load and prices as well as gray-box thermodynamic modeling. A Pareto optimal schedule is defined as the schedule that maximizes profit to the REP and minimizes its risk of low profits. We show how much benefit REPs stand to gain by following an optimal load schedule and how much they stand to lose by enacting DR events at the wrong times. © 2019, The Authors. All rights reserved.

关键词： Sales

Bullen’s parameter as a seismic observable for spin crossovers in the lower mantle

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arXiv 2017年

作者： Valencia-Cardona, Juan J. Williams, Quentin Shukla, Gaurav Wentzcovitch, Renata M. Scientific Computing Program University of Minnesota MinneapolisMN United States Department of Earth and Planetary Sciences University of California Santa Cruz Santa CruzCA United States Department of Earth Ocean and Atmospheric Science Florida State University TallahasseeFL United States Department of Applied Physics and Applied Mathematics Columbia University New York CityNY United States Lamont-Doherty Earth Observatory Columbia University PalisadesNY United States

Elastic anomalies produced by the spin crossover in ferropericlase have been documented by both first principles calculations and high pressure-temperature experiments. The predicted signature of this spin crossover in the lower mantle is, however, subtle and difficult to geophysically observe within the mantle. Indeed, global seismic anomalies associated with spin transitions have not yet been recognized in seismologic studies of the deep mantle. A sensitive seismic parameter is needed to determine the presence and amplitude of such a spin crossover signature. The effects of spin crossovers on Bullen’s parameter, η, are assessed here for a range of compositions, thermal profiles, and lateral variations in temperature within the lower mantle. Velocity anomalies associated with the spin crossover in ferropericlase span a depth range near 1,000 km for typical mantle temperatures. Positive excursions of Bullen’s parameter with a maximum amplitude of ∼ 0.03 are calculated to be present over a broad depth range within the mid-to-deep lower mantle: these are largest for peridotitic and harzburgitic compositions. These excursions are highest in amplitude for model lower mantles with large lateral thermal variations, and with cold downwellings having longer lateral length-scales relative to hot upwellings. We conclude that predicted deviations in Bullen’s parameter due to the spin crossover in ferropericlase for geophysically relevant compositions may be sufficiently large to resolve in accurate seismic inversions of this parameter, and could shed light on both the lateral variations in temperature at depth within the lower mantle, and the amount of ferropericlase at depth. Copyright © 2017, The Authors. All rights reserved.

关键词： Seismology

Characterising acute and chronic care needs: insights from the Global Burden of Disease Study 2019

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Nature communications 2025年第1期16卷 4235-4235页

作者： Cecilia Anza-Ramirez J. Jaime Miranda Benedetta Armocida Jorge César Correia Harriette Gillian Christine Van Spall David Beran Amirali Aali Kalkidan Hassen Abate Semagn Mekonnen Abate Cristiana Abbafati Mohsen Abbasi-Kangevari Zeinab Abbasi-Kangevari Zahra Aryan Sina Azadnajafabad Mohammadreza Azangou-Khyavy Seyyed-Hadi Ghamari Mohammad Keykhaei Javad Khanali Sara Momtazmanesh Fateme Montazeri Shayan Rahmani Mohammad-Mahdi Rashidi Nazila Rezaei Negar Rezaei Sahar Saeedi Moghaddam Hossein Hassanian-Moghaddam Ali-Asghar Kolahi Ali Nikoobar Hedayat Abbastabar Ahmed M. Abdel-Azeem Michael Abdelmasseh Juan Sanabria Sherief Abd-Elsalam Ahmed Abdelwahab Gholamreza Abdoli Mohammad Abdollahi Meriem Abdoun Deldar Morad Abdulah Abu Yousuf Md Abdullah Ame Mehadi Abdurehman Getachew Abebe Aidin Abedi Chirag P. Doshi Vida Abedi Hassan Abidi Richard Gyan Aboagye Hassan Abolhassani Nima Rezaei Lucas Guimarães Abreu Michael R. M. Abrigo Yonas Derso Abtew Hiwa Abubaker Ali Eman Abu-Gharbieh Hiba Jawdat Barqawi Rabih Halwani Maha Mohamed Saber-Ayad Iman M. Talaat Ahmed Abu-Zaid Manfred Mario Kokou Accrombessi Juan Manuel Acuna Denberu Eshetie Adane Tigist Demssew Adane Isaac Yeboah Addo Giovanni Addolorato Oluwafemi Atanda Adeagbo Victor Adekanmbi Miracle Ayomikun Adesina Isaac Iyinoluwa Olufadewa Olatunji O. Adetokunboh Daniel Adedayo Adeyinka Qorinah Estiningtyas Sakilah Adnani Aanuoluwapo Adeyimika Afolabi Olayinka Stephen Ilesanmi Muhammad Sohail Afzal Saira Afzal Gina Agarwal Prerna Agarwal Pradyumna Agasthi Anurag Agrawal Marcela Agudelo-Botero Adolfo Martinez-Valle Bright Opoku Ahinkorah Aqeel Ahmad Sajjad Ahmad Sohail Ahmad Tauseef Ahmad Ali Ahmadi Siamak Sabour Keivan Ahmadi Sanjay Basu Sepideh Ahmadi Ali Ahmed Shaun Wen Huey Lee Ayman Ahmed Haroon Ahmed Jivan Qasim Ahmed Gahin Abdulraheem Tayib Yahya Yahya Luai A. Ahmed Iffat Elbarazi Syed Mahboob Shah Janardhana P. Aithala Marjan Ajami Budi Aji Hossein Akbarialiabad Yibeltal Akelew Meisam Akhlaghdoust Elham Jamshidi Addis Aklilu Azene Tesfaye Melat Woldemariam Maxwell Ak CRONICAS Center of Excellence in Chronic Diseases Universidad Peruana Cayetano Heredia Lima Peru School of Medicine Universidad Peruana Cayetano Heredia Lima Peru Sydney School of Public Health Faculty of Medicine and Health University of Sydney Sydney NSW Australia Faculty of Epidemiology and Population Health London School of Hygiene & Tropical Medicine London UK Division of Tropical and Humanitarian Medicine University of Geneva Geneva Switzerland Department of Cardiovascular Endocrine-metabolic Diseases and Aging Istituto Superiore di Sanità Rome Italy Division of Endocrinology Diabetology Nutrition and Therapeutic Patient Education Department of Medicine Geneva University Hospitals Geneva Switzerland Department of Medicine and Department of Health Research Evidence and Impact McMaster University Hamilton ON Canada Research Institute of St. Joe’s Hamilton ON Canada Population Health Research Institute Hamilton Canada Geneva University Hospitals Geneva Switzerland Faculty of Medicine Mashhad University of Medical Sciences Mashhad Iran Department of Nutrition and Dietetics Jimma University Jimma Ethiopia Anesthesiology Department Dilla University Addis Ababa Ethiopia Department of Juridical and Economic Studies La Sapienza University Rome Italy Non-Communicable Diseases Research Center Tehran University of Medical Sciences Tehran Iran Social Determinants of Health Research Center Shahid Beheshti University of Medical Sciences Tehran Iran Brigham and Women’s Hospital Harvard University Boston MA USA Students’ Scientific Research Center (SSRC) Tehran University of Medical Sciences Tehran Iran School of Medicine Tehran University of Medical Sciences Tehran Iran School of Medicine Shahid Beheshti University of Medical Sciences Tehran Iran Endocrinology and Metabolism Research Institute Tehran University of Medical Sciences Tehran Iran Chapter of Addiction Medicine University of Sydney Sydney NSW Australia Advanced Diagnostic and Intervent

Chronic care manages long-term, progressive conditions, while acute care addresses short-term conditions. Chronic conditions increasingly strain health systems, which are often unprepared for these demands. This study examines the burden of conditions requiring acute versus chronic care, including sequelae. Conditions and sequelae from the Global Burden of Diseases Study 2019 were classified into acute or chronic care categories. Data were analysed by age, sex, and socio-demographic index, presenting total numbers and contributions to burden metrics such as Disability-Adjusted Life Years (DALYs), Years Lived with Disability (YLD), and Years of Life Lost (YLL). Approximately 68% of DALYs were attributed to chronic care, while 27% were due to acute care. Chronic care needs increased with age, representing 86% of YLDs and 71% of YLLs, and accounting for 93% of YLDs from sequelae. These findings highlight that chronic care needs far exceed acute care needs globally, necessitating health systems to adapt accordingly. © 2025. The Author(s).

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Genetic analysis of over 1 million people identifies 535 new loci associated with blood pressure traits (vol 50, pg 1412, 2018)

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NATURE GENETICS 2018年第12期50卷 1755-1755页

作者： Evangelou, Evangelos Warren, Helen R. Mosen-Ansorena, David Mifsud, Borbala Pazoki, Raha Gao, He Ntritsos, Georgios Dimou, Niki Cabrera, Claudia P. Karaman, Ibrahim Fu Liang Ng Evangelou, Marina Witkowska, Katarzyna Tzanis, Evan Hellwege, Jacklyn N. Giri, Ayush Edwards, Digna R. Velez Sun, Yan V. Cho, Kelly Gaziano, J. Michael Wilson, Peter W. F. Tsao, Philip S. Kovesdy, Csaba P. Esko, Tonu Magi, Reedik Milani, Lili Almgren, Peter Boutin, Thibaud Debette, Stephanie Ding, Jun Giulianini, Franco Holliday, Elizabeth G. Jackson, Anne U. Li-Gao, Ruifang Lin, Wei-Yu Luan, Jian'an Mangino, Massimo Oldmeadow, Christopher Prins, Bram Peter Qian, Yong Sargurupremraj, Muralidharan Shah, Nabi Surendran, Praveen Theriault, Sebastien Verweij, Niek Willems, Sara M. Zhao, Jing-Hua Amouyel, Philippe Connell, John de Mutsert, Renee Doney, Alex S. F. Farrall, Martin Menni, Cristina Morris, Andrew D. Noordam, Raymond Pare, Guillaume Poulter, Neil R. Shields, Denis C. Stanton, Alice Thom, Simon Abecasis, Goncalo Amin, Najaf Arking, Dan E. Ayers, Kristin L. Barbieri, Caterina M. Batini, Chiara Bis, Joshua C. Blake, Tineka Bochud, Murielle Boehnke, Michael Boerwinkle, Eric Boomsma, Dorret I. Bottinger, Erwin P. Braund, Peter S. Brumat, Marco Campbell, Archie Campbell, Harry Chakravarti, Aravinda Chambers, John C. Chauhan, Ganesh Ciullo, Marina Cocca, Massimiliano Collins, Francis Cordell, Heather J. Davies, Gail de Borst, Martin H. de Geus, Eco J. Deary, Ian J. Deelen, Joris Del Greco, Fabiola M. Demirkale, Cumhur Yusuf Dorr, Marcus Ehret, Georg B. Elosua, Roberto Enroth, Stefan Erzurumluoglu, A. Mesut Ferreira, Teresa Franberg, Mattias Franco, Oscar H. Gandin, Ilaria Gasparini, Paolo Giedraitis, Vilmantas Gieger, Christian Girotto, Giorgia Goel, Anuj Gow, Alan J. Gudnason, Vilmundur Guo, Xiuqing Gyllensten, Ulf Hamsten, Anders Harris, Tamara B. Harris, Sarah E. Hartman, Catharina A. Havulinna, Aki S. Hicks, Andrew A. Hofer, Edith Hofman, Albert Hottenga, Jouke-Jan Huffman, Jennifer E. Hwang, Shih-Jen Ingelsson, Erik James, Alan Jansen Department of Epidemiology and Biostatistics Imperial College London London UK Department of Hygiene and Epidemiology University of Ioannina Medical School Ioannina Greece William Harvey Research Institute Barts and The London School of Medicine and Dentistry Queen Mary University of London London UK National Institute for Health Research Barts Cardiovascular Biomedical Research Center Queen Mary University of London London UK MRC-PHE Centre for Environment and Health Imperial College London London UK Department of Mathematics Imperial College London London UK Division of Epidemiology Department of Medicine Institute for Medicine and Public Health Vanderbilt Genetics Institute Vanderbilt University Medical Center Tennessee Valley Healthcare System (626)/Vanderbilt University Nashville TN USA Vanderbilt Genetics Institute Vanderbilt Epidemiology Center Department of Obstetrics and Gynecology Vanderbilt University Medical Center Tennessee Valley Health Systems VA Nashville TN USA Department of Epidemiology Emory University Rollins School of Public Health Atlanta GA USA Department of Biomedical Informatics Emory University School of Medicine Atlanta GA USA Massachusetts Veterans Epidemiology Research and Information Center (MAVERIC) VA Boston Healthcare System Boston MA USA Division of Aging Department of Medicine Brigham and Women’s Hospital Department of Medicine Harvard Medical School Boston MA USA Atlanta VAMC and Emory Clinical Cardiovascular Research Institute Atlanta GA USA VA Palo Alto Health Care System Division of Cardiovascular Medicine Stanford University School of Medicine Stanford CA USA Nephrology Section Memphis VA Medical Center and University of Tennessee Health Science Center Memphis TN USA Estonian Genome Center University of Tartu Tartu Estonia Program in Medical and Population Genetics Broad Institute of Harvard and MIT Cambridge MA USA Department Clinical Sciences Malmö Lund University Malmö Sweden MRC Human Genetics Un

High blood pressure is a highly heritable and modifiable risk factor for cardiovascular disease. We report the largest genetic association study of blood pressure traits (systolic, diastolic and pulse pressure) to date in over 1 million people of European ancestry. We identify 535 novel blood pressure loci that not only offer new biological insights into blood pressure regulation but also highlight shared genetic architecture between blood pressure and lifestyle exposures. Our findings identify new biological pathways for blood pressure regulation with potential for improved cardiovascular disease prevention in the future.

关键词： Cardiovascular diseases Genome informatics Genome-wide association studies