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arXiv 2022年

作者： Jiang, Bo Liu, Ya-Feng Key Laboratory for NSLSCS of Jiangsu Province School of Mathematical Sciences Nanjing Normal University Nanjing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Projecting the distance measures onto a low-dimensional space is an efficient way of mitigating the curse of dimensionality in the classical Wasserstein distance using optimal transport. The obtained maximized distance is referred to as projection robust Wasserstein (PRW) distance. In this paper, we equivalently reformulate the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints. We propose a Riemannian exponential augmented Lagrangian method (ReALM) with a global convergence guarantee to solve this problem. Compared with the existing approaches, ReALM can potentially avoid too small penalty parameters. Moreover, we propose a framework of inexact Riemannian gradient descent methods to solve the subproblems in ReALM efficiently. In particular, by using the special structure of the subproblem, we give a practical algorithm named as the inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS). The remarkable features of iRBBS lie in that it performs a flexible number of Sinkhorn iterations to compute an inexact gradient with respect to the projection matrix of the problem and adopts the Barzilai-Borwein stepsize based on the inexact gradient information to improve the performance. We show that iRBBS can return an ǫ-stationary point of the original PRW distance problem within O(ǫ−3) iterations. Extensive numerical results on synthetic and real datasets demonstrate that our proposed ReALM as well as iRBBS outperform the state-of-the-art solvers for computing the PRW *** Codes 65K10, 90C26, 90C47 Copyright © 2022, The Authors. All rights reserved.

关键词： Constrained optimization

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A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks

arXiv

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arXiv 2024年

作者： Punke, Maik Salvalaglio, Marco Voigt, Axel Wise, Steven M. Institute of Scientific Computing TU Dresden Dresden01062 Germany Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany Department of Mathematics The University of Tennessee KnoxvilleTN37996 United States

We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The thermal compatibility condition, as well as a positive entropy-production property, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within a positive entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification. Copyright © 2024, The Authors. All rights reserved.

关键词： Crystal lattices

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A Finite Element Framework for Solving the Density-Gradient Model

A Finite Element Framework for Solving the Density-Gradient ...

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International Conference on Simulation of Semiconductor Processes and Devices (SISPAD)

作者： Pengcong Mu Tao Cui Lijun Xu Kun Luo Zhiqiang Li Zhenhua Wu Institute of Microelectronics Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China LSEC NCMIS Institute of Computational Mathematics and Scientific Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China School of Pyhsics Zhejiang University Hangzhou China

ISBN: (数字)9798331516352

ISBN: (纸本)9798331516369

This paper presents a positive-preserving, stable finite element scheme for the density-gradient (DG) model. An ef-ficient Newton-Krylov solver is designed to address the nonlinear coupled discrete system. Simulation results for gate-all-around (GAA) devices demonstrate the robustness and effectiveness of the proposed scheme. Notably, the simulation time using our method is only half that of the Sentaurus Device, highlighting its superior computational efficiency.

关键词： Semiconductor device modeling computational modeling Simulation Gallium arsenide Field effect transistors Logic gates Robustness Semiconductor process modeling Finite element analysis computational efficiency

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Smooth approximation of feedback laws for infinite horizon control problems with non-smooth value functions

arXiv

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arXiv 2023年

作者： Kunisch, Karl Vásquez-Varas, Donato Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstraße 69 Upper Austria Linz4040 Austria Institute of Mathematics and Scientific Computing University of Graz Heinrichstraße 36 Styria Graz8010 Austria

In this work the synthesis of approximate optimal and smooth feedback laws for infinite horizon optimal control problems is addressed. In this regards, Lp type error bounds of the approximating smooth feedback laws are derived, depending on either the C1 norm of the value function or its semi-concavity. These error bounds combined with the existence of a Lyapunov type function are used to prove the existence of an approximate optimal sequence of smooth feedback laws. Moreover, we extend this result to the Hölder continuous case by a diagonalization argument combined with the Moreau envelope. It is foreseen that these error bounds could be applied to study the convergence of synthesis of feedback laws via data driven machine learning methods. Additionally, we provide an example of an infinite horizon optimal control problem for which the value functions is non-differentiable but Lipschitz continuous. We point out that in this example no restrictions on either the controls or the trajectories are *** Codes 49L12, 49L25, 49N35, 93B52, 35D40 © 2023, CC BY.

关键词： Learning systems

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Novel semi-explicit symplectic schemes for nonseparable stochastic Hamiltonian systems

arXiv

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arXiv 2024年

作者： Hong, Jialin Hou, Baohui Sun, Liying 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 Shanghai University Shanghai200444 China Academy for Multidisciplinary Studies Capital Normal University Beijing100048 China

In this manuscript, we propose efficient stochastic semi-explicit symplectic schemes tailored for nonseparable stochastic Hamiltonian systems (SHSs). These semi-explicit symplectic schemes are constructed by introducing augmented Hamiltonians and using symmetric projection. In the case of the artificial restraint in augmented Hamiltonians being zero, the proposed schemes also preserve quadratic invariants, making them suitable for developing semi-explicit charge-preserved multi-symplectic schemes for stochastic cubic Schrödinger equations with multiplicative noise. Through numerical experiments that validate theoretical results, we demonstrate that the proposed stochastic semi-explicit symplectic scheme, which features a straightforward Newton iteration solver, outperforms the traditional stochastic midpoint scheme in terms of effectiveness and accuracy. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

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Influential Slot and Tag Selection in Billboard Advertisement

arXiv

引用

arXiv 2024年

作者： Ali, Dildar Gupta, Tejash Banerjee, Suman Prasad, Yamuna Department of Computer Science and Engineering Indian Institute of Technology Jammu Jammu & Kashmir Jammu India Department of Mathematics and Scientific Computing National Institute of Technology Hamirpur Himachal Pradesh Hamirpur India

The selection of influential billboard slots remains an important problem in billboard advertisements. Existing studies on this problem have not considered the case of context-specific influence probability. To bridge this gap, in this paper, we introduce the Context Dependent Influential Billboard Slot Selection Problem. First, we show that the problem is NP-hard. We also show that the influence function holds the bi-monotonicity, bi-submodularity, and non-negativity properties. We propose an orthant-wise Stochastic Greedy approach to solve this problem. We show that this method leads to a constant factor approximation guarantee. Subsequently, we propose an orthant-wise Incremental and Lazy Greedy approach. In a generic sense, this is a method for maximizing a bi-submodular function under the cardinality constraint, which may also be of independent interest. We analyze the performance guarantee of this algorithm as well as time and space complexity. The proposed solution approaches have been implemented with real-world billboard and trajectory datasets. We compare the performance of our method with many baseline methods, and the results are reported. Our proposed orthant-wise stochastic greedy approach leads to significant results when the parameters are set properly with reasonable computational overhead. © 2024, CC BY.

关键词： Stochastic systems

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Detecting and Exploiting Unit Commitment Structures in MIPs

Detecting and Exploiting Unit Commitment Structures in MIPs

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International Conference on Power and Energy Technology (ICPET)

作者： Zhao-Gang Su Sheng-Jie Chen Yu-Fei Li Liang Chen Caixia Kou Zhi Cai Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China College of Sciences Beijing University of Posts and Telecommunications Beijing China Beijing Key Laboratory of Research and System Evaluation of Power Dispatching Automation Technology China Electric Power Research Institute Beijing China

ISBN: (数字)9798350375855

ISBN: (纸本)9798350375862

The unit commitment (UC) problem has been extensively researched in the literature, which is typically formulated as a mixed integer programming (MIP) problem. However, current studies lack effective methods to identify potential UC problem structures within a general MIP problem, making it challenging to leverage well-established valid inequalities for UC problems to accelerate the solution process. In this paper, we present a novel detection method that automatically identifies UC structures within an MIP problem by analyzing the relationships between variables and constraints. Moreover, we enhance the MIP formulation by incorporating three well-studied classes of valid inequalities as cutting planes, based on the identified UC structures. Our experiments demonstrate that our proposed UC detection method greatly improves computational efficacy of a standard MIP solver compared to the default setting.

关键词： Integer programming Production Generators Time factors Standards

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Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach

arXiv

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arXiv 2022年

作者： Cui, Jianbo Hong, Jialin Sun, Liying Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Hong Kong Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Institute of Applied Physics and Computational Mathematics Beijing100094 China

In this paper, we propose and analyze semi-implicit numerical schemes for the stochastic wave equation (SWE) with general nonlinearity and multiplicative noise. These numerical schemes, called stochastic scalar auxiliary variable (SAV) schemes, are constructed by transforming the considered SWE into a higher dimensional stochastic system with a stochastic SAV. We prove that they can be solved explicitly and preserve the modified energy evolution law and the regularity structure of the original system. These structure-preserving properties are the keys to overcoming the mutual effect of the noise and nonlinearity. By proving new regularity estimates of the introduced SAV, we establish the strong convergence rate of stochastic SAV schemes and the further fully-discrete schemes with the finite element method in spatial direction. To the best of our knowledge, this is the first result on the construction and strong convergence of semi-implicit energy-preserving schemes for nonlinear SWE. © 2022, CC BY.

关键词： Stochastic systems

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Non-Iterative Recovery from Nonlinear Observations using Generative Models

arXiv

引用

arXiv 2022年

作者： Liu, Jiulong Liu, Zhaoqiang LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences 100190 China Department of Computer Science National University of Singapore Singapore

In this paper, we aim to estimate the direction of an underlying signal from its nonlinear observations following the semi-parametric single index model (SIM). Unlike conventional compressed sensing where the signal is assumed to be sparse, we assume that the signal lies in the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. This is mainly motivated by the tremendous success of deep generative models in various real applications. Our reconstruction method is non-iterative (though approximating the projection step may use an iterative procedure) and highly efficient, and it is shown to attain the near-optimal statistical rate of order √(k log L)/m, where m is the number of measurements. We consider two specific instances of the SIM, namely noisy 1-bit and cubic measurement models, and perform experiments on image datasets to demonstrate the efficacy of our method. In particular, for the noisy 1-bit measurement model, we show that our non-iterative method significantly outperforms a state-of-the-art iterative method in terms of both accuracy and efficiency. Copyright © 2022, The Authors. All rights reserved.

关键词： Iterative methods

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CSI Sensing from Heterogeneous User Feedbacks: A Constrained Phase Retrieval Approach

arXiv

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arXiv 2022年

作者： Li, Lei Zeng, Xing Liu, Ya-Feng Xu, Yanqing Chang, Tsung-Hui The School of Science and Engineering The Chinese University of Hong Kong Shenzhen China Huawei Technologies Ltd. Shanghai China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

This paper investigates the downlink channel state information (CSI) sensing in 5G heterogeneous networks composed of user equipments (UEs) with different feedback capabilities. We aim to enhance the CSI accuracy of UEs only affording the low-resolution Type-I codebook. While existing works have demonstrated that the task can be accomplished by solving a phase retrieval (PR) formulation based on the feedback of precoding matrix indicator (PMI) and channel quality indicator (CQI), they need many feedback rounds. In this paper, we propose a novel CSI sensing scheme that can significantly reduce the feedback overhead. Our scheme involves a novel parameter dimension reduction design by exploiting the spatial consistency of wireless channels among nearby UEs, and a constrained PR (CPR) formulation that characterizes the feasible region of CSI by the PMI information. To address the computational challenge due to the non-convexity and the large number of constraints of CPR, we develop a two-stage algorithm that firstly identifies and removes inactive constraints, followed by a fast first-order algorithm. The study is further extended to multi-carrier systems. Extensive tests over DeepMIMO and QuaDriGa datasets showcase that our designs greatly outperform existing methods and achieve the high-resolution Type-II codebook performance with a few rounds of feedback. Copyright © 2022, The Authors. All rights reserved.

关键词： Channel state information

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