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SSRN 2025年

作者： Ye, Jialu Tan, Chaogui Xia, Yizhang Hou, Zhanglu Liu, Yuan Zou, Juan Hunan Engineering Research Center of intelligent System Optimization and Security Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan National Applied Mathematics Center China Xiangtan University China

Population co-evolution strategies are widely used to handle constrained multi-objective optimization problems (CMOPs). However, existing coevolutionary algorithms oversimplify population collaboration and are rigid in evolving the auxiliary population, ignoring the importance of maintaining population diversity, especially for CMOPs with irregular feasible regions. To tackle this issue, we propose a new dual-population evolutionary algorithm, denoted as AACMO, which attempts to mine the relational features between the unconstrained Pareto front (UPF) and the constrained Pareto front (CPF) to better adapt to CMOPs with various constraints. Specifically, the method is categorized into two phases: a learning phase and an evolving phase. First, the main population (MP) aims to quickly learn the relationships between the UPF and the CPF by leveraging the advantages of different operators, namely, genetic algorithm operators and differential evolution operators, during the learning phase. Secondly, two auxiliary strategies are designed to collaborate with the MP during the evolving phase. These strategies are capable of employing a more effective co-evolution method to assist the MP in maintaining diversity, based on the degree of alignment between the learned UPF and CPF at the end of the learning phase. The effectiveness of AACMO is confirmed through comparative analysis with eight state-of-the-art algorithms across four CMOP benchmark suites. © 2025, The Authors. All rights reserved.

关键词： Optimization algorithms

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Comparing Constraint Evaluation Methods for Shape-Constrained Regression 19thth

Comparing Constraint Evaluation Methods for Shape-Constrain...

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19th International Conference on Computer Aided Systems Theory, EUROCAST 2024

作者： Haider, Christian Bachinger, Florian Holzinger, Florian de França, Fabrício Olivetti Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Hagenberg Austria Johannes Kepler University Linz Austria Center for Mathematics Computing and Cognition Federal University of ABC Santo André Brazil

ISBN: (纸本)9783031829512

Shape-constrained regression is an important desideratum of data-based modeling when you want to enforce your model to possess an expected behavior despite the intrinsic noise of the collected data. Conventional data-based modeling approaches are solely reliant on empirical data, and thus, often fail to incorporate the essential physical constraints inherent to the underlying systems. This leads to a lack of trust in the model and a reduction of explanatory power. Recognizing these limitations of traditional data-based methodologies, the integration of shape constraints, derived from domain expertise or fundamental physical principles, emerges as a promising extension to enhance the quality of models. In this paper, we distinguish between single-objective and multi-objective approaches, as well as soft and hard constraint methods to evaluate the constraint violations of models. In the context of this research, the primary focus is on single-objective approaches that incorporate an expanded scope of features and dynamics for constraint handling. Instead of strictly enforcing hard constraints and discarding solutions solely based on constraint violation, the paper presents a dynamic method for calculating constraint violation and prediction error. The presented approach involves an incremental increase in the weighting of constraint violation during the modeling process, achieving an initial, wide-ranging exploration of the solution space followed by a comprehensive investigation of potential models through an in-depth search. Furthermore, we want to explore the critical issue of premature stagnation, a phenomenon wherein the search for a conformant model, plateaus before reaching an acceptable local optima solution. This paper tries to address this challenge through different strategies to maintain a certain diversity of solutions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Regression analysis

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Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem

arXiv

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arXiv 2023年

作者： Kirk, Keegan L.A. Masri, Rami Riviere, Beatrice Department of Computational and Applied Mathematics Rice University Houston United States Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway

The mixed form of the Cahn-Hilliard equations is discretized by the hybridizable discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the numerical solution is obtained. The scheme is proved to be unconditionally stable. Convergence of the method is obtained by deriving a priori error estimates that are valid for the Ginzburg-Lindau chemical energy density and for convex domains. The paper also contains discrete functional tools, namely discrete Agmon and Gagliardo-Nirenberg inequalities, which are proved to be valid in the hybridizable discontinuous Galerkin *** Codes 65M15 (Primary) 65M60 (Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Numerical methods

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A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection

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Communications in Computational Physics 2023年第4期33卷 1164-1188页

作者： Chengjie Zhan Zhenhua Chai Baochang Shi Ping Jiang Shaoning Geng Dongke Sun School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074P.R.China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and TechnologyWuhan 430074P.R.China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074P.R.China The State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhan 430074P.R.China School of Mechanical Engineering Southeast UniversityNanjing 211189P.R.China

In this work,we proposed a diffuse-interface model for the dendritic growth with thermosolutal *** this model,the sharp boundary between the fluid and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface,which is described by the order parameter,and the diffuse-interface based governing equations for the dendritic growth are *** solve the model for the dendritic growth with thermosolutal convection,we also developed a diffuse-interface multirelaxation-time lattice Boltzmann(LB)*** this method,the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction,and the treatment on the complex fluid-solid interface can be *** addition,four LB models are designed for the phase-field equation,concentration equation,temperature equation and the Navier-Stokes equations in a unified ***,we performed some simulations of the dendritic growth to test the present diffuse-interface LB method,and found that the numerical results are in good agreements with some previous works.

关键词： Dendritic growth diffuse interface lattice Boltzmann method phase-field method.

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On the -differential spectra of two classes of power functions over finite fields

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Applicable Algebra in Engineering, Communication and computing 2025年 1-30页

作者： Liu, Qian Huang, Zhiwei Chen, Zhixiong Jiang, Rong Zhang, Liupiao Key Laboratory of Information Security of Network Systems College of Computer and Data Science Fuzhou University Fuzhou China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan China Yunnan Key Laboratory of Service Computing Yunnan University of Finance and Economics Kunming China Fujian Key Laboratory of Financial Information Processing Putian University Putian China School of Computer Science and Technology Dongguan University of Technology Dongguan China

Recently, a new concept called multiplicative differential was introduced by Ellingsen et al. [7]. As an extension of the differential uniformity, it is theoretically appealing to determine the properties of c-differential uniformity and the corresponding c-differential spectrum. In this paper, based on certain quadratic character sums and two special elliptic curves over $$\mathbb {F}_p$$ , the $$(-1)$$ -differential spectra of the following two classes of power functions over $$\mathbb {F}_{p^n}$$ is completely determined: (1) $$f_1(x)=x^{\frac{p^n+3}{2}}$$ , where $$p>3$$ and $$p\equiv 3\pmod 4$$ ; (2) $$f_2(x)=x^{p^n-3}$$ , where $$p>3$$ . The obtained result shows that the $$(-1)$$ -differential spectra of $$f_1(x)$$ and $$f_2(x)$$ can be expressed explicitly in terms of n. Moreover, an upper bound of the c-differential uniformity of $$f_2(x)$$ is given.

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Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning

arXiv

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arXiv 2024年

作者： Chang, Tyler Gillette, Andrew Maulik, Romit Mathematics and Computer Science Division Argonne National Laboratory United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Information Sciences and Technology Department The Pennsylvania State University United States

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. In this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently;(2) comparative performance among distinct interpolants can aid in validation goals;(3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository. © 2024, CC BY-NC-SA.

关键词： Interpolation

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SUNDIALS Time Integrators for Exascale Applications with Many Independent ODE Systems

arXiv

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arXiv 2024年

作者： Balos, Cody J. Day, Marc Esclapez, Lucas Felden, Anne M. Gardner, David J. Hassanaly, Malik Reynolds, Daniel R. Rood, Jon Sexton, Jean M. Wimer, Nicholas T. Woodward, Carol S. Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Department of Mathematics Southern Methodist University United States National Renewable Energy Laboratory United States Lawrence Berkeley National Laboratory United States TU Delft Netherlands

Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world's largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger "outer-loop" time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently. Copyright © 2024, The Authors. All rights reserved.

关键词： Initial value problems

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Memristive feature and mechanism induced by laser-doping in defect-free 2D semiconductor materials

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Journal of Semiconductors 2024年第7期45卷 85-91页

作者： Xiaoshan Du Shu Wang Qiaoxuan Zhang Shengyao Chen Fengyou Yang Zhenzhou Liu Zhengwei Fan Lijun Ma Lei Wang Lena Du Zhongchang Wang Cong Wang Bing Chen Qian Liu College of Electronic and Information Engineering Shandong University of Science and TechnologyQingdao 266590China National Center for Nanoscience and Technology&University of Chinese Academy of Sciences Beijing 100190China Hebei University of Water Resources and Electric Engineering Electrical Automation Department Cangzhou 061001China The MOE Key Laboratory of Weak-Light Nonlinear Photonics and International Sino-Slovenian Join Re-search Center on Liquid Crystal Pho-tonics TEDA Institute of Applied Physics and School of PhysicsNankai UniversityTianjin 300457China College of Mathematics and Physics Shandong Advanced Optoelectronic Materials and Technologies Engineering LaboratoryQingdao Uni-versity of Science and TechnologyQingdao 266061China Department of Physics Capital Normal UniversityBeijing 100048China Department of Advanced Materials and Computing International Iberian Nanotechnology Laboratory(INL)4715-330 BragaPortugal College of Mathematics and Physics Beijing University of Chemical TechnologyBeijing 100029China

Memristors as non-volatile memory devices have gained numerous attentions owing to their advantages in storage,in-memory computing, synaptic applications, etc. In recent years, two-dimensional(2D) materials with moderate defects have been discovered to exist memristive feature. However, it is very difficult to obtain moderate defect degree in 2D materials, and studied on modulation means and mechanism becomes urgent and essential. In this work, we realized memristive feature with a bipolar switching and a configurable on/off ratio in a two-terminal MoS_(2) device(on/off ratio ~100), for the first time, from absent to present using laser-modulation to few-layer defect-free MoS_(2)(about 10 layers), and its retention time in both high resistance state and low resistance state can reach 2×10^(4) s. The mechanism of the laser-induced memristive feature has been cleared by dynamic Monte Carlo simulations and first-principles calculations. Furthermore, we verified the universality of the laser-modulation by investigating other 2D materials of TMDs. Our work will open a route to modulate and optimize the performance of 2D semiconductor memristive devices.

关键词： 2D-material memristor laser doping laser direct writing memristive mechanism

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Fast θ -Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis

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Computational and applied mathematics 2023年第3期42卷

作者： Wang, Mengjie Dai, Xinjie Yu, Yanyan Xiao, Aiguo Hunan Key Laboratory for Computation and Simulation in Science and Engineering National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Yunnan University Yunnan Kunming650504 China

In this paper, a fast θ-Maruyama method is proposed for solving stochastic Volterra integral equations of convolution type with singular and Hölder continuous kernels based on the sum-of-exponentials approximation. Furthermore, the average storage O(N) and the calculation cost O(N2) of θ-Maruyama scheme are reduced to O(log N) and O(Nlog N) for T 1 or O(log 2N) and O(Nlog 2N) for T≈ 1 , respectively, which implies that the fast θ-Maruyama scheme is confirmed to improve the computational efficiency of the θ-Maruyama method. Under the local Lipschitz and linear growth conditions, strong convergence of the given numerical scheme are obtained. Then, for the linear test equation, we show the asymptotic behavior of solutions in mean square sense. Further, we obtain the explicit structure of the stability matrices and some numerical results of the mean-square stability for the fast θ-Maruyama method applied to the linear test equation. Finally, some numerical experiments are also given to illustrate the effectiveness of the method. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

关键词： Computational efficiency

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A Medical Pre-diagnosis Scheme Based on Neural Network and Inner Product Function Encryption

A Medical Pre-diagnosis Scheme Based on Neural Network and I...

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Electronic Communication and Artificial Intelligence (IWECAI), International Workshop on

作者： Xu Cui Hao Liu Min Tang Yihong Ma School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin China Center for Applied Mathematics of Guangxi (GUET) Guilin China

Artificial neural networks are widely used in various fields, such as intelligent road networks, Internet of Things, and smart medical systems due to their ability to process large amounts of data in parallel, store information in a distributed manner, and self-organize and self-learn. Cloud computing technology has further expanded the development of neural network applications. However, user data often contains sensitive information, and once the data management right is transferred to the cloud, it faces serious security and privacy issues. In the medical field, privacy-preserving implementation of classification algorithms is crucial for ensuring the privacy of electronic medical diagnosis services. Current privacy-preserving medical pre-diagnosis schemes based on homomorphic encryption impose a significant computational and communication burden on users and servers. This paper proposes an efficient privacy-preserving medical pre-diagnosis scheme based on neural networks and inner product function encryption that protects user privacy during pre-diagnosis while having small computational and communication overheads.

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