检索结果-内蒙古大学图书馆

Mean-field theory for double-well systems on degree-heterogeneous networks

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Kundu, Prosenjit MacLaren, Neil G. Kori, Hiroshi Masuda, Naoki Department of Mathematics State University of New York BuffaloNY14260-2900 United States Department of Complexity Science and Engineering The University of Tokyo Chiba277-8561 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY14260-5030 United States

Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system’s dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosses a certain threshold. Tipping elements in such systems may interact with each other as a network, and understanding the behavior of interacting tipping elements is a challenge because of the high dimensionality originating from the network. Here we develop a degree-based mean-field theory for a prototypical double-well system coupled on a network with the aim of understanding coupled tipping dynamics with a low-dimensional description. The method approximates both the onset of the tipping point and the position of equilibria with a reasonable accuracy. Based on the developed theory and numerical simulations, we also provide evidence for multistage tipping point transitions in networks of double-well systems. © 2022, CC BY.

关键词： Mean field theory

Multi-index Sequential Monte Carlo ratio estimators for Bayesian Inverse problems

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Law, Kody J.H. Walton, Neil Yang, Shangda Jasra, Ajay School of Mathematics University of Manchester ManchesterM13 9PL United Kingdom Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous across science and engineering applications, for example in the context of Bayesian inference where a physics-based model governed by an intractable partial differential equation (PDE) appears in the likelihood. A multi-index Sequential Monte Carlo (MISMC) method is used to construct ratio estimators which provably enjoy the complexity improvements of multi-index Monte Carlo (MIMC) as well as the efficiency of Sequential Monte Carlo (SMC) for inference. In particular, the proposed method provably achieves the canonical complexity of MSE−1, while single level methods require MSE−ξ for ξ > 1. This is illustrated on examples of Bayesian inverse problems with an elliptic PDE forward model in 1 and 2 spatial dimensions, where ξ = 5/4 and ξ = 3/2, respectively. It is also illustrated on more challenging log Gaussian process models, where single level complexity is approximately ξ = 9/4 and multilevel Monte Carlo (or MIMC with an inappropriate index set) gives ξ = 5/4 + ω, for any ω > 0, whereas our method is again canonical. We also provide novel theoretical verification of the product-form convergence results which MIMC requires for Gaussian processes built in spaces of mixed regularity defined in the spectral domain, which facilitates acceleration with fast Fourier transform methods via a cumulant embedding strategy, and may be of independent interest in the context of spatial statistics and machine learning. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

On the particle approximation of lagged Feynman–Kac formulae

学校读者我要写书评

暂无评论

Stochastic Processes and their Applications 2025年 188卷

作者： Awadelkarim, Elsiddig Caffarel, Michel Del Moral, Pierre Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia University of Toulouse CNRS-Lab. de Chimie et Physique Quantiques Toulouse31062 France Centre de Recherche Inria Bordeaux Sud-Ouest Talence33405 France School of Data Science The Chinese University of Hong Kong Shenzhen Shenzhen China

In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman–Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function. The typical application considered here is the computation of eigenvalues associated with non-negative operators as found, for example, in physics or particle simulation of rare-events. We focus on a novel lagged approximation of this invariant measure, based upon the introduction of a ratio of time-averaged Feynman–Kac marginals associated with a positive operator iterated l∈N times;a lagged Feynman–Kac formula. This estimator and its approximation using Diffusion Monte Carlo (DMC) are commonly used in the physics literature. In short, DMC is an iterative algorithm involving N∈N particles or walkers simulated in parallel, that undergo sampling and resampling operations. In this work, it is shown that for the DMC approximation of the lagged Feynman–Kac formula, one has an almost sure characterization of the L1-error as the time parameter (iteration) goes to infinity and this is at most of O(exp{−κl}/N), for κ>0. In addition a non-asymptotic in time, and time uniform L1−bound is proved which is O(l/N). We also prove a novel central limit theorem to give a characterization of the exact asymptotic in time variance. This analysis demonstrates that the strategy used in physics, namely, to run DMC with N and l small and, for long time enough, is mathematically justified. Our results also suggest how one should choose N and l in practice. We emphasize that these results are not restricted to physical applications;they have broad relevance to the general problem of particle simulation of the Feynman–Kac formula, which is utilized in a great variety of scientific and engineering fields. © 2025 Elsevier B.V.

关键词： Iterative methods

Layer-dependent optically induced spin polarization in InSe

学校读者我要写书评

暂无评论

Physical Review B 2023年第11期107卷 115304-115304页

作者： Jovan Nelson Teodor K. Stanev Dmitry Lebedev Trevor LaMountain J. Tyler Gish Hongfei Zeng Hyeondeok Shin Olle Heinonen Kenji Watanabe Takashi Taniguchi Mark C. Hersam Nathaniel P. Stern Applied Physics Program Northwestern University Evanston Illinois 60208 USA Department of Physics and Astronomy Northwestern University Evanston Illinois 60208 USA Department of Material Science and Engineering Northwestern University Evanston Illinois 60208 USA Computational Science Division Argonne National Laboratory Lemont Illinois 60439 USA Material Science Division Argonne National Laboratory Lemont Illinois 60439 USA Research Center for Functional Materials National Institute for Materials Science 1-1 Namiki Tsukuba 305-0044 Japan International Center for Materials Nanoarchitectonics National Institute for Materials Science 1-1 Namiki Tsukuba 305-0044 Japan Department of Chemistry Northwestern University Evanston Illinois 60208 USA Department of Electrical Engineering and Computer Science Northwestern University Evanston Illinois 60208 USA

Optical control of spin in semiconductors has been pioneered using nanostructures of III-V and II-VI semiconductors, but the emergence of two-dimensional van der Waals materials offers an alternative low-dimensional platform for spintronic phenomena. Indium selenide (InSe), a group-III monochalcogenide van der Waals material, has shown promise for optoelectronics due to its high electron mobility, tunable direct band gap, and quantum transport. In addition to these confirmed properties, there are predictions of spin-dependent optical selection rules, suggesting the potential for all-optical excitation and control of spin in a two-dimensional layered material. Despite these predictions, layer-dependent optical spin phenomena in InSe have yet to be explored. Here, we present measurements of layer-dependent optical spin dynamics in few-layer and bulk InSe. Polarized photoluminescence reveals layer-dependent optical orientation of spin, thereby demonstrating the optical selection rules in few-layer InSe. Spin dynamics are also studied in many-layer InSe using time-resolved Kerr rotation spectroscopy. By applying out-of-plane and in-plane static magnetic fields for polarized emission measurements and Kerr measurements, respectively, the g factor for InSe was extracted. Further investigations are done by calculating precession values using a k·p model, which is supported by ab initio density functional theory. Comparison of predicted precession rates with experimental measurements highlights the importance of excitonic effects in InSe for understanding spin dynamics. Optical orientation of spin is an important prerequisite for optospintronic phenomena and devices, and these first demonstrations of layer-dependent optical excitation of spins in InSe lay the foundation for combining layer-dependent spin properties with advantageous electronic properties found in this material.

关键词： Magneto-optics Spin dynamics Chalcogenides Layered semiconductors Van der Waals systems Density functional theory Kerr effect Photoluminescence k dot p method

Dimension reduction of dynamical systems on networks with leading and non-leading eigenvectors of adjacency matrices

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Masuda, Naoki Kundu, Prosenjit Department of Mathematics State University of New York BuffaloNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY14260-5030 United States

Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensional dynamical system whose behavior approximates the observables of the original dynamical system that are weighted linear summations of the state variables at the different nodes. Recently proposed methods use the leading eigenvector of the adjacency matrix of the network as the mixture weights to obtain such observables. In the present study, we explore performances of this type of one-dimensional reductions of dynamical systems on networks when we use non-leading eigenvectors of the adjacency matrix as the mixture weights. Our theory predicts that non-leading eigenvectors can be more efficient than the leading eigenvector and enables us to select the eigenvector minimizing the error. We numerically verify that the optimal non-leading eigenvector outperforms the leading eigenvector for some dynamical systems and networks. We also argue that, despite our theory, it is practically better to use the leading eigenvector as the mixture weights to avoid misplacing the bifurcation point too distantly and to be resistant against dynamical noise. © 2022, CC BY.

关键词： Eigenvalues and eigenfunctions

Early Warnings for Multistage Transitions in Dynamics on Networks

学校读者我要写书评

暂无评论

arXiv 2022年

作者： MacLaren, Neil G. Kundu, Prosenjit Masuda, Naoki Department of Mathematics State University of New York BuffaloNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY14260-5030 United States

Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multistage transitions in which some nodes experience a regime shift earlier than others as an environment gradually changes. Here we investigate early warning signals for networked systems undergoing a multistage transition. We found that knowledge of both the ongoing multistage transition and network structure enables us to calculate effective early warning signals for multistage transitions. Furthermore, we found that small subsets of nodes could anticipate transitions as well as or even better than using all the nodes. Even if we fix the network and dynamical system, no single best subset of nodes provides good early warning signals, and a good choice of sentinel nodes depends on the tipping direction and the current stage of the dynamics within a multistage transition, which we systematically characterize. © 2022, CC BY.

关键词： Dynamics

A Bottom-Up, Multi-Scale Model for Transient Mass Transport of Redox-Active Species Through Porous Electrodes Beyond the Pseudo-Steady Limit

学校读者我要写书评

暂无评论

SSRN

SSRN 2022年

作者： Hamid, Md Abdul Smith, Kyle C. Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Materials Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 United States Computational Science and Engineering Program University of Illinois at Urbana-Champaign UrbanaIL61801 United States Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign UrbanaIL61801 United States

A transient, multi-scale model is introduced to capture the dynamic response of redox-active electrolyte flowing through porous electrodes under time-dependent current input. Unlike conventional models with time-invariant mass transfer coefficient, certain frequency-dependent transfer functions (TFs) are introduced to embed transient pore-scale transport physics into an up-scaled model. One of the introduced TFs is a spectral Sherwood number, that extends the film law of mass transfer to transient conditions. Another TF is introduced to capture the acceleration/suppression of solute advection resulting from inhomogeneity in local concentration distribution. The frequency dependence of these TFs is demonstrated for electrodes comprised of solid cylinders in crossflow. Three distinct spectral regions are observed, where with increasing frequency a transition from lagless response to semi-infinite Warburg response occurs. The results show orders of magnitude higher mass transfer rate for fast-changing applied current. These TFs are then embedded into an up-scaled model to obtain the time domain response of flow batteries. Analysis of concentration polarization and the average reactant concentration inside electrodes is used to construct non-dimensional maps of their operation space. From this analysis we find that fast current fluctuations can be sustained at conditions exceeding the limiting current that is expected for pseudo-steady operation. © 2022, The Authors. All rights reserved.

关键词： Flow batteries

Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Jiang, Ziyang Zheng, Tongshu Liu, Yiling Carlson, David Department of Civil and Environmental Engineering Duke University United States Division of Natural and Applied Science Duke Kunshan University China Program in Computational Biology and Bioinformatics Duke University School of Medicine United States Department of Civil and Environmental Engineering Department of Biostatistics and Bioinformatics Department of Computer Science Duke University United States

It is challenging to guide neural network (NN) learning with prior knowledge. In contrast, many known properties, such as spatial smoothness or seasonality, are straightforward to model by choosing an appropriate kernel in a Gaussian process (GP). Many deep learning applications could be enhanced by modeling such known properties. For example, convolutional neural networks (CNNs) are frequently used in remote sensing, which is subject to strong seasonal effects. We propose to blend the strengths of NNs and the clear modeling capabilities of GPs by using a composite kernel that combines a kernel implicitly defined by a neural network with a second kernel function chosen to model known properties (e.g., seasonality). We implement this idea by combining a deep network and an efficient mapping function based on either Nyström approximation or random Fourier features, which we call Implicit Composite Kernel (ICK). We then adopt a sample-then-optimize approach to approximate the full GP posterior distribution. We demonstrate that ICK has superior performance and flexibility on both synthetic and real-world datasets including a remote sensing dataset. The ICK framework can be used to include prior information into neural networks in many applications. © 2022, CC BY.

关键词： Remote sensing

Ogden Material Calibration via Magnetic Resonance Cartography, Parameter Sensitivity, and Variational System Identification

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Nikolov, Denislav P. Srivastava, Siddhartha Abeid, Bachir A. Scheven, Ulrich M. Arruda, Ellen M. Garikipati, Krishna Estrada, Jonathan B. Department of Mechanical Engineering University of Michigan United States Department of Biomedical Engineering University of Michigan United States Program in Macromolecular Science and Engineering University of Michigan United States Department of Mathematics University of Michigan United States Michigan Institute for Computational Discovery and Eng. University of Michigan United States

Contemporary material characterisation techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterisation problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely-used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability, and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully 3D displacement fields acquired in silicone elastomers with our recently-developed magnetic resonance cartography (MR-u) technique on the order of > 20, 000 points per sample, we leverage PDE-constrained optimisation as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric, and discuss the implications for experimental design. © 2022, CC BY-NC-ND.

关键词： Inverse problems