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A parameter estimator based on Smoluchowski-Kramers approximation 1

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arXiv 2018年

作者： He, Ziying Duan, Jinqiao Cheng, Xiujun Center for Mathematical Sciences School of Mathematics and Statistics Hubei Key Laboratory for Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States

We devise a simplified parameter estimator for a second order stochastic differential equation by a first order system based on the Smoluchowski-Kramers approximation. We establish the consistency of the estimator by using Γ-convergence theory. We further illustrate our estimation method by an experimentally studied movement model of a colloidal particle immersed in water under conservative force and constant diffusion. Copyright © 2018, The Authors. All rights reserved.

关键词： Differential equations

Characterization of the most probable transition paths of stochastic dynamical systems with stable Lévy noise

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arXiv 2018年

作者： Huang, Yuanfei Chao, Ying Yuan, Shenglan Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States

This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric α-stable Lévy motion (0 Copyright © 2018, The Authors. All rights r... 详细信息

关键词： Brownian movement

Benchmark modeling and 3D applications of solidification and macro-segregation based on an operator-splitting and fully decoupled scheme with term-wise matrix assembly

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arXiv 2023年

作者： Feng, Xiaoyu Chen, Huangxin Yu, Bo Sun, Shuyu Thuwal23955-6900 Saudi Arabia School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen361005 China School of Mechanical Engineering Beijing Institute of Petrochemical Technology Beijing102617 China

The solidification and macro-segregation problem involving unsteady multiphysics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The quantitative prediction of phase change, chemical heterogeneities, and multi-phase and multi-component flows plays critical roles in many natural scenarios and industrial applications that involve many disciplines, like material, energy, and even planet science. In view of this, some scholars and research institutions have called for more contributors to join the benchmark analysis of solidification and segregation problems. Our work proposes an operator-splitting and matrix-based method to avoid non-linear systems. Also, the combination of vectorization and forward equation-based matrix assembly techniques enhances the implementability of extensions of 3D applications. Lastly, the novel scheme is well validated through a bunch of 2D and 3D benchmark cases. The numerical results also illustrate that this method can ensure accurate prediction and adequately capture the physical details of phenomena caused by the solutally and thermally driven flow, which include channel segregation, the formation of freckles, edge effect, aspect ratio effect, and 3D effect. Copyright © 2023, The Authors. All rights reserved.

关键词： Solidification

Heterogeneous Domain Decomposition Methods for Fluid-Structure Interaction Problems

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Lecture Notes in Computational Science and engineering 2007年 55卷 41-52页

作者： Deparis, Simone Discacciati, Marco Fourestey, Gilles Quarteroni, Alfio Mechanical Engineering Department Massachusetts Institute of Technology 77 Mass Ave Cambridge 02139 MA United States EPFL IACS - Chair of Modeling and Scientific Computing Lausanne CH-1015 Switzerland Politecnico di Milano MOX P.zza Leonardo da Vinci 32 Milano 20133 Italy

In this note, we propose Steklov-Poincaré iterative algorithms (mutuated from the analogy with heterogeneous domain decomposition) to solve fluidstructure interaction problems. Although our framework is very gene... 详细信息

ISBN: (纸本)9783540344681

关键词： Domain decomposition methods

HYDRODYNAMICS FOR ASYMMETRIC SIMPLE EXCLUSION ON A FINITE SEGMENT WITH GLAUBER-TYPE SOURCE

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arXiv 2024年

作者： Xu, Lu Zhao, Linjie Gran Sasso Science Institute AQ L'Aquila67100 Italy School of Mathematics and Statistics Huazhong University of Science & Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the hydrodynamic limit for the particle density at the hyperbolic space-time scale and obtain the entropy solution to a boundary-driven quasilinear conservation law with a source term. Different from the usual boundary conditions introduced in [3, 20], discontinuity (boundary layer) does not formulate at the boundaries due to the strong relaxation scheme. Copyright © 2024, The Authors. All rights reserved.

关键词： Hydrodynamics

Benchmark modeling and 3d Applications of Solidification and Macro-Segregation Based on an Operator-Splitting and Fully Decoupled Scheme with Term-Wise Matrix Assembly

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SSRN

SSRN 2023年

The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and constituent transfers among solid, mushy, and liquid phase regions. The quantitative prediction of phase change, chemical heterogeneities, and multi-phase and multi-component flows plays critical roles in many natural scenarios and industrial applications that involve many disciplines, like material, energy, and even planet science. In view of this, some scholars and research institutions have called for more contributors to join the benchmark analysis of solidification and segregation problems. Our work proposes fully decoupled and iterative schemes based on operator-splitting and matrix-based ideas to avoid solving non-linear systems directly. Also, the combination of direct vectorization and equation-based forward matrix assembly techniques enhances the implementability and efficiency of extensions to 3D applications. Lastly, the novel scheme is well validated through a bunch of 2D and 3D benchmark cases. The numerical results also illustrate that this method can ensure accurate prediction and efficient computation. It adequately captures the physical details of phenomena caused by the solutally and thermally driven flow, which include channel segregation, the formation of freckles, edge effect, aspect ratio effect, and 3D effect. © 2023, The Authors. All rights reserved.

关键词： Solidification

Bridging Fairness Gaps: A (Conditional) Distance Covariance Perspective in Fairness Learning

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arXiv 2024年

作者： Huang, Ruifan Liu, Haixia School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan Hubei China School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China

We bridge fairness gaps from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We enhance fairness by incorporating sample (conditional) distance covariance as a manageable penalty term into the machine learning process. Additionally, we present the matrix form of empirical (conditional) distance covariance for parallel calculations to enhance computational efficiency. Theoretically, we provide a proof for the convergence between empirical and population (conditional) distance covariance, establishing necessary guarantees for batch computations. Through experiments conducted on a range of real-world datasets, we have demonstrated that our method effectively bridges the fairness gap in machine learning. Copyright © 2024, The Authors. All rights reserved.

关键词： Contrastive Learning

Local Precipitation Forecast with LSTM for Greenhouse Environmental Control

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Local Precipitation Forecast with LSTM for Greenhouse Enviro...

Pervasive Artificial Intelligence (ICPAI), International Conference on

作者： Hsing-Chuan Hsieh Yi-Wei Chiu Yong-Xiang Lin Ming-Hwi Yao Yuh-Jye Lee Institute of Statistics National Chiao Tung University Hsinchu Taiwan Institute of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu Taiwan Agricultural Engineering Division Taiwan Agricultural Research Institute Council of Agriculture Executive Yuan Taichung Taiwan Research Center for Information Technology Innovation Academia Sinica Taipei Taiwan

ISBN: (数字)9781665404839

ISBN: (纸本)9781665404846

With the rise of AI technology, it can be applied to smart greenhouse. In our research, we design a prevention mechanism against instant heavy rainfall using Long Short-Term Memory (LSTM) networks to forecast the local precipitation at the next hour near the greenhouse. Besides, missing data and imbalanced data issues are also tackled. Our experiments show that linear interpolation is enough to deal with sporadic missing data. Moreover, two approaches of imbalanced data handling can also enhance the performance of our proposed seasonal LSTM models, including oversampling methods which manipulate the imbalanced training data, as well as cost-sensitive learning methods which modify the loss function in some way. Finally, we also provide the reference result for the greenhouse farmers, so as to decide how much trade-off between Recall and Accuracy they can bear. This is done by tuning parameters related to imbalanced data handling techniques.

关键词： Green products Meteorology Data models Rain Air pollution Predictive models Logic gates

Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues

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Physical Review E 2023年第1期108卷 015304-015304页

作者： Zhenhua Chai (柴振华) Xiaolei Yuan (袁晓垒) Baochang Shi (施保昌) School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China College of Mathematics and Information Science Hebei University Baoding 071002 China

In this paper, we develop a general rectangular multiple-relaxation-time lattice Boltzmann (RMRT-LB) method for the Navier-Stokes equations (NSEs) and nonlinear convection-diffusion equation (NCDE) by extending our recent unified framework of the multiple-relaxation-time lattice Boltzmann (MRT-LB) method [Chai and Shi, Phys. Rev. E 102, 023306 (2020)], where an equilibrium distribution function (EDF) [Lu et al., Philos. Trans. R. Soc. A 369, 2311 (2011)] on a rectangular lattice is utilized. The anisotropy of the lattice tensor on a rectangular lattice leads to anisotropy of the third-order moment of the EDF, which is inconsistent with the isotropy of the viscous stress tensor of the NSEs. To eliminate this inconsistency, we extend the relaxation matrix related to the dynamic and bulk viscosities. As a result, the macroscopic NSEs can be recovered from the RMRT-LB method through the direct Taylor expansion method. Whereas the rectangular lattice does not lead to the change of the zero-, first- and second-order moments of the EDF, the unified framework of the MRT-LB method can be directly applied to the NCDE. It should be noted that the RMRT-LB model for NSEs can be derived on the rDdQq (q discrete velocities in d-dimensional space, d≥1) lattice, including rD2Q9, rD3Q19, and rD3Q27 lattices, while there are no rectangular D3Q13 and D3Q15 lattices within this framework of the RMRT-LB method. Thanks to the block-lower triangular relaxation matrix introduced in the unified framework, the RMRT-LB versions (if existing) of the previous MRT-LB models can be obtained, including those based on raw (natural) moment, central moment, Hermite moment, and central Hermite moment. It is also found that when the parameter cs is an adjustable parameter in the standard or rectangular lattice, the present RMRT-LB method becomes a kind of MRT-LB method for the NSEs and NCDE, and the commonly used MRT-LB models on the DdQq lattice are only its special cases. We also perform some numeric

关键词： Lattice-Boltzmann methods