检索结果-内蒙古大学图书馆

SSRN 2023年

作者： Wang, Jian Liu, Haitao Zhang, Jing Xiao, Qingbo Wang, Chong Zhang, Yongzheng Liu, Meinan Kang, Qi Jia, Lujie Wang, Dong Li, Qi Duan, Wenhui Adenusi, Henry Passerini, Stefano Zhang, Yuegang Lin, Hongzhen i-Lab & CAS Key Laboratory of Nanophotonic Materials and Devices Suzhou Institute of Nano-tech and Nano-bionics Chinese Academy of Sciences Suzhou215123 China UlmD89081 Germany KarlsruheD-76021 Germany Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Materials Science and Engineering Xi’an University of Technology Xi’an710048 China Department of Physics Tsinghua University Beijing100084 China State Key Laboratory of Chemical Engineering East China University of Science and Technology Shanghai200237 China Department of Polymer Science and Engineering Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Automobile Materials of MOE School of Materials Science and Engineering Jilin University Changchun130012 China The University of Hong Kong Department of Chemistry Pokfulam Road Hong Kong Hong Kong Quantum AI Lab 17 Science Park West Avenue Hong Kong Sapienza University of Rome Chemistry Department P. A. Moro 5 Rome00185 Italy

Understanding of interfacial Li+ solvation shell structures and dynamic evolution at the electrode/electrolyte interface is requisite for developing high-energy-density Li batteries. Herein, the reorganization of Li+ solvation shell at the sulfur/electrolyte interface along with the presence of a trace amount of lithium polysulfides is verified by in-situ sum frequency generation (SFG) spectroscopy together with density functional theory (DFT) calculations. Both the spectroelectrochemical and DFT calculation results reveal a strongly competitive anion adsorption of the polysulfide anion additive against the pristine electrolyte anions on the sulfur cathode surface, reorganizing the interfacial local solvation shell structure facilitating rapid Li ion transfer and conduction. Meanwhile, the evolution of the SFG signals along with the discharging/charging cycle exhibits improved reversibility, indicating the transformation of the inner Helmholtz plane layer into a stable molecular-layer polysulfide interphase rather than a dynamic diffusion layer. Consequently, applications in practical Li-S batteries reveal the capacity and cycling stability of the corresponding cells are significantly enhanced. Our work provides a methodology using in-situ SFG for probing solvation reorganization of charge carriers at electrochemical interfaces. © 2023, The Authors. All rights reserved.

关键词： Negative ions

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Quality of internal representation shapes learning performance in feedback neural networks

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Physical Review Research 2021年第1期3卷 013176-013176页

作者： Lee Susman Francesca Mastrogiuseppe Naama Brenner Omri Barak Interdisciplinary Program in Applied Mathematics Technion Israel Institute of Technology Haifa 32000 Israel Network Biology Research Laboratories Technion Israel Institute of Technology Haifa 32000 Israel Gatsby Computational Neuroscience Unit University College London London W1T 4JG United Kingdom Department of Chemical Engineering Technion Israel Institute of Technology Haifa 32000 Israel Rappaport Faculty of Medicine Technion Israel Institute of Technology Haifa 32000 Israel

A fundamental feature of complex biological systems is the ability to form feedback interactions with their environment. A prominent model for studying such interactions is reservoir computing, where learning acts on low-dimensional bottlenecks. Despite the simplicity of this learning scheme, the factors contributing to or hindering the success of training in reservoir networks are in general not well understood. In this work, we study nonlinear feedback networks trained to generate a sinusoidal signal, and analyze how learning performance is shaped by the interplay between internal network dynamics and target properties. By performing exact mathematical analysis of linearized networks, we predict that learning performance is maximized when the target is characterized by an optimal, intermediate frequency which monotonically decreases with the strength of the internal reservoir connectivity. At the optimal frequency, the reservoir representation of the target signal is high-dimensional, desynchronized, and thus maximally robust to noise. We show that our predictions successfully capture the qualitative behavior of performance in nonlinear networks. Moreover, we find that the relationship between internal representations and performance can be further exploited in trained nonlinear networks to explain behaviors which do not have a linear counterpart. Our results indicate that a major determinant of learning success is the quality of the internal representation of the target, which in turn is shaped by an interplay between parameters controlling the internal network and those defining the task.

关键词： Learning theory Artificial neural networks Dynamical systems Neuronal network models

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Simulating Cardiac Fluid Dynamics in the Human Heart

arXiv

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arXiv 2023年

作者： Davey, Marshall Puelz, Charles Rossi, Simone Smith, Margaret Anne Wells, David R. Sturgeon, Gregory M. Segars, W. Paul Vavalle, John P. Peskin, Charles S. Griffith, Boyce E. University of North Carolina Chapel HillNC United States Department of Pediatrics-Cardiology Baylor College of Medicine Texas Children’s Hospital HoustonTX United States Department of Mathematics University North Carolina Chapel HillNC United States Department of Radiology Duke University Medical Center DurhamNC United States Division of Cardiology Department of Medicine University of North Carolina School of Medicine Chapel HillNC United States Courant Institute of Mathematical Sciences New York University New YorkNY United States Departments of Mathematics and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin, flexible valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions. However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the cardiac valves are limited in their abilities to predict valve performance, resolve fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac fluid dynamics in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart’s microstructure. Further, it is the first fluid-structure interaction model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and predicts fine-scale flow features. None of these outputs are prescribed;instead, they emerge from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical devices or clinical interventions. They also can serve as platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients. Copyright © 2023, The Authors. All rights reserved.

关键词： Heart

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An optimal algorithm for strict circular seriation

arXiv

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arXiv 2021年

作者： Armstrong, Santiago Guzmán, Cristóbal Long, Carlos A. Sing Institute for Mathematical and Computational Engineering Pontificia Universidad Católica de Chile Santiago Chile Anid - Millennium Science Initiative Program Millennium Nucleus Center for the Discovery of Structures in Complex Data Santiago Chile Department of Applied Mathematics University of Twente Netherlands Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Santiago Chile

We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between n objects, and the goal is to find a circular order of the objects in a manner that is consistent with their dissimilarity. This problem is a generalization of the classical linear seriation problem where the goal is to find a linear order, and for which optimal O(n2) algorithms are known. Our contributions can be summarized as follows. First, we introduce circular Robinson matrices as the natural class of dissimilarity matrices for the circular seriation problem. Second, for the case of strict circular Robinson dissimilarity matrices we provide an optimal O(n2) algorithm for the circular seriation problem. Finally, we propose a statistical model to analyze the well-posedness of the circular seriation problem for large n. In particular, we establish O(log(n)/n) rates on the distance between any circular ordering found by solving the circular seriation problem to the underlying order of the model, in the Kendall-tau *** Codes 68R01, 05C85, 05C50, 05C25, 65C20 Copyright © 2021, The Authors. All rights reserved.

关键词： Trees (mathematics)

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Multi-hump Collapsing Solutions in the Nonlinear Schrödinger Problem: Existence, Stability and Dynamics

arXiv

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arXiv 2025年

作者： Chapman, S. Jon Kavousanakis, Mihalis Charalampidis, Efstathios G. Kevrekidis, Ioannis G. Kevrekidis, Panayotis G. Mathematical Institute University of Oxford AWB ROQ Woodstock Road OxfordOX2 6GG United Kingdom School of Chemical Engineering National Technical University of Athens Athens15780 Greece Department of Mathematics and Statistics Computational Science Research Center San Diego State University San DiegoCA92182-7720 United States Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Department of Mathematics and Statistics University of Massachusetts AmherstMA01003-4515 United States Department of Physics University of Massachusetts AmherstMA01003 United States

In the present work we examine multi-hump solutions of the nonlinear Schrödinger equation in the blowup regime of the one-dimensional model with power law nonlinearity, bearing a suitable exponent of σ > 2. We find that families of such solutions exist for arbitrary pulse numbers, with all of them bifurcating from the critical case of σ = 2. Remarkably, all of them involve "bifurcations from infinity", i.e., the pulses come inward from an infinite distance as the exponent σ increases past the critical point. The position of the pulses is quantified and the stability of the waveforms is also systematically examined in the so-called "co-exploding frame". Both the equilibrium distance between the pulse peaks and the point spectrum eigenvalues associated with the multi-hump configurations are obtained as a function of the blowup rate G theoretically, and these findings are supported by detailed numerical computations. Finally, some prototypical dynamical scenarios are explored, and an outlook towards such multi-hump solutions in higher dimensions is provided. Copyright © 2025, The Authors. All rights reserved.

关键词： Schrodinger equation

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DeePMD-kit v3: A Multiple-Backend Framework for Machine Learning Potentials

arXiv

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arXiv 2025年

作者： Zeng, Jinzhe Zhang, Duo Peng, Anyang Zhang, Xiangyu He, Sensen Wang, Yan Liu, Xinzijian Bi, Hangrui Li, Yifan Cai, Chun Zhang, Chengqian Du, Yiming Zhu, Jia-Xin Mo, Pinghui Huang, Zhengtao Zeng, Qiyu Shi, Shaochen Qin, Xuejian Yu, Zhaoxi Luo, Chenxing Ding, Ye Liu, Yun-Pei Shi, Ruosong Wang, Zhenyu Bore, Sigbjørn Løland Chang, Junhan Deng, Zhe Ding, Zhaohan Han, Siyuan Jiang, Wanrun Ke, Guolin Liu, Zhaoqing Lu, Denghui Muraoka, Koki Oliaei, Hananeh Singh, Anurag Kumar Que, Haohui Xu, Weihong Xu, Zhangmancang Zhuang, Yong-Bin Dai, Jiayu Giese, Timothy J. Jia, Weile Xu, Ben York, Darrin M. Zhang, Linfeng Wang, Han School of Artificial Intelligence and Data Science Unversity of Science and Technology of China Hefei China AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100871 China University of Chinese Academy of Sciences Beijing China Baidu Inc. Beijing China Department of Computer Science University of Toronto TorontoON Canada Department of Chemistry Princeton University PrincetonNJ08540 United States University of Chinese Academy of Sciences Beijing100871 China State Key Laboratory of Physical Chemistry of Solid Surfaces iChEM College of Chemistry and Chemical Engineering Xiamen University Xiamen361005 China College of Integrated Circuits Hunan University Changsha410082 China State Key Laboratory of Advanced Technology for Materials Synthesis and Processing Center for Smart Materials and Device Integration School of Material Science and Engineering Wuhan University of Technology Wuhan430070 China College of Science National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Extreme Matter and Applications National University of Defense Technology Changsha410073 China ByteDance Research Beijing100098 China Ningbo Institute of Materials Technology and Engineering Chinese Academy of Sciences Ningbo315201 China College of Materials Science and Opto-Electronic Technology University of Chinese Academy of Sciences Beijing100049 China Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education College of Chemistry Beijing Normal University Beijing100875 China Department of Geosciences Princeton University PrincetonNJ08544 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States IKKEM Fujian Xiamen361005 China Graduate

In recent years, machine learning potentials (MLPs) have become indispensable tools in physics, chemistry, and materials science, driving the development of software packages for molecular dynamics (MD) simulations and related applications. These packages, typically built on specific machine learning frameworks such as TensorFlow, PyTorch, or JAX, face integration challenges when advanced applications demand communication across different frameworks. The previous TensorFlow-based implementation of DeePMD-kit exemplified these limitations. In this work, we introduce DeePMD-kit version 3, a significant update featuring a multi-backend framework that supports TensorFlow, PyTorch, JAX, and PaddlePaddle backends, and demonstrate the versatility of this architecture through the integration of other MLPs packages and of Differentiable Molecular Force Field. This architecture allows seamless backend switching with minimal modifications, enabling users and developers to integrate DeePMD-kit with other packages using different machine learning frameworks. This innovation facilitates the development of more complex and interoperable workflows, paving the way for broader applications of MLPs in scientific research. Copyright © 2025, The Authors. All rights reserved.

关键词： Molecular dynamics

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Position: Bayesian deep learning is needed in the age of large-scale AI 24

Position: Bayesian deep learning is needed in the age of lar...

引用

Proceedings of the 41st International Conference on Machine Learning

作者： Theodore Papamarkou Maria Skoularidou Konstantina Palla Laurence Aitchison Julyan Arbel David Dunson Maurizio Filippone Vincent Fortuin Philipp Hennig José Miguel Hernández-Lobato Aliaksandr Hubin Alexander Immer Theofanis Karaletsos Mohammad Emtiyaz Khan Agustinus Kristiadi Yingzhen Li Stephan Mandt Christopher Nemeth Michael A. Osborne Tim G. J. Rudner David Rügamer Yee Whye Teh Max Welling Andrew Gordon Wilson Ruqi Zhang Department of Mathematics The University of Manchester Manchester UK Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge Spotify London UK Computational Neuroscience Unit University of Bristol Bristol UK Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany and Department of Computer Science Technical University of Munich Munich Germany and Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge UK Department of Mathematics University of Oslo Oslo Norway and Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative California Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London UK Department of Computer Science UC Irvine Irvine Department of Mathematics and Statistics Lancaster University Lancaster UK Department of Engineering Science University of Oxford Oxford UK Center for Data Science New York University New York Munich Center for Machine Learning Munich Germany and Department of Statistics LMU Munich Munich Germany DeepMind London UK and Department of Statistics University of Oxford Oxford UK Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences and Center for Data Science Computer Science Department New York University New York Department of Computer Science Purdue University West Lafayette

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

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On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method

arXiv

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arXiv 2021年

作者： Lee, Jae H. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering Johns Hopkins University BaltimoreMD United States Institute for Computational Medicine Johns Hopkins University BaltimoreMD United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method’s performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretizations combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta function). Earlier work with this methodology suggested that such coarse structural meshes can yield imp

关键词： Fluid structure interaction

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A Nodal Immersed Finite Element-Finite Difference Method

arXiv

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arXiv 2021年

作者： Wells, David R. Vadala-Roth, Ben Lee, Jae H. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Westborough MA United States Department of Mechanical Engineering Institute for Computational Medicine Johns Hopkins University BaltimoreMD United States Department of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States Center for Drug Evaluation and Research U.S. Food and Drug Administration Silver SpringMD United States

The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. The IFED method uses a finite element (FE) method to approximate the stresses, forces, and structural deformations on a structural mesh and a finite difference (FD) method to approximate the momentum and enforce the incompressibility of the entire fluid-structure system on a Cartesian grid. The fundamental approach used by this method follows the immersed boundary framework for modeling fluid-structure interaction (FSI), in which a force spreading operator prolongs structural forces to a Cartesian grid, and a velocity interpolation operator restricts a velocity field defined on that grid back onto the structural mesh. With an FE structural mechanics framework, force spreading first requires that the force itself be projected onto the finite element space. Similarly, velocity interpolation requires projecting velocity data onto the FE basis functions. Consequently, evaluating either coupling operator requires solving a matrix equation at every time step. Mass lumping, in which the projection matrices are replaced by diagonal approximations, has the potential to accelerate this method considerably. This paper provides both numerical and computational analyses of the effects of this replacement for evaluating the force projection and for the IFED coupling operators. Constructing the coupling operators also requires determining the locations on the structure mesh where the forces and velocities are sampled. Here we show that sampling the forces and velocities at the nodes of the structural mesh is equivalent to using lumped mass matrices in the IFED coupling operators. A key theoretical result of our analysis is that if both of these approaches are used together, the IFED method permits the use of lumped mass matrices derived from nodal quadrature rules for any standard interpolatory element. This is different from s

关键词： Fluid structure interaction

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A hybrid semi-Lagrangian cut cell method for advection-diffusion problems with robin boundary conditions in moving domains

arXiv

引用

arXiv 2021年

作者： Barrett, Aaron Fogelson, Aaron L. Griffith, Boyce E. Department of Mathematics University of Utah Salt Lake CityUT United States Departments of Mathematics and Bioengineering University of Utah Salt Lake CityUT United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

We present a new discretization approach to advection-diffusion problems with Robin boundary conditions on complex, time-dependent domains. The method is based on second order cut cell finite volume methods introduced by Bochkov et al. [8] to discretize the Laplace operator and Robin boundary condition. To overcome the small cell problem, we use a splitting scheme along with a semi-Lagrangian method to treat advection. We demonstrate second order accuracy in the L1, L2, and L∞norms for both analytic test problems and numerical convergence studies. We also demonstrate the ability of the scheme to convert one chemical species to another across a moving boundary. © 2021, CC BY-SA.

关键词： Advection

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