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On Cyclic Finite-State Approximation of Data-Driven Systems

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arXiv 2019年

作者： Vides, Fredy Scientific Computing Innovation Center Department of Applied Mathematics Universidad Nacional Autónoma de Honduras UNAH Honduras Graduate Program in Structural Engineering Universidad Tecnológica Centroamericana UNITEC Honduras

In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix approximation problems that appear in the fields of system identification and model predictive control, for data-driven systems and processes. The research reported in this document is focused on finite-state approximation of data-driven systems. Some numerical implementations of the aforementioned techniques in the simulation and model predictive control of some generic data-driven systems, that are related to electrical signal transmission models, are outlined.93B28, 47N70 (primary) and 93C57, 93B40 (secondary) Copyright © 2019, The Authors. All rights reserved.

关键词： Singular value decomposition

A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

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arXiv 2023年

作者： Herrala, Olli Gabriel, Steven A. Oliveira, Fabricio Ekholm, Tommi Aalto University Department of Mathematics and Systems Analysis Espoo Finland University of Maryland Department of Mechanical Engineering/Applied Mathematics Statistics & Scientific Computing Program College ParkMD United States Norwegian University of Science and Technology Department of Industrial Economics and Technology Management Trondheim Norway Finnish Meteorological Institute Helsinki Finland

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed methods, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio. Copyright © 2023, The Authors. All rights reserved.

关键词： Energy resources

Improved Dwarf Mongoose Optimization for Constrained Engineering Design Problems

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Journal of Bionic Engineering 2023年第3期20卷 1263-1295页

作者： Jeffrey O.Agushaka Absalom E.Ezugwu Oyelade N.Olaide Olatunji Akinola Raed Abu Zitar Laith Abualigah School of Mathematics Statisticsand Computer ScienceUniversity of KwaZulu-NatalKing Edward AvenuePietermaritzburg CampusPietermaritzburg3201KwaZulu-NatalSouth Africa Department of Computer Science Federal University of LafiaLafia950101Nigeria Unit for Data Science and Computing North-West University11 Hoffman StreetPotchefstroom2520South Africa Sorbonne Center of Artificial Intelligence Sorbonne University-Abu Dhabi38044Abu DhabiUnited Arab Emirates Hourani Center for Applied Scientific Research Al-Ahliyya Amman UniversityAmman19328Jordan Faculty of Information Technology Middle East UniversityAmman11831Jordan Faculty of Information Technology Applied Science Private UniversityAmman11931Jordan School of Computer Sciences Universiti Sains Malaysia11800Pulau PinangMalaysia

This paper proposes a modified version of the Dwarf Mongoose Optimization Algorithm (IDMO) for constrained engineering design problems. This optimization technique modifies the base algorithm (DMO) in three simple but effective ways. First, the alpha selection in IDMO differs from the DMO, where evaluating the probability value of each fitness is just a computational overhead and contributes nothing to the quality of the alpha or other group members. The fittest dwarf mongoose is selected as the alpha, and a new operator ω is introduced, which controls the alpha movement, thereby enhancing the exploration ability and exploitability of the IDMO. Second, the scout group movements are modified by randomization to introduce diversity in the search process and explore unvisited areas. Finally, the babysitter's exchange criterium is modified such that once the criterium is met, the babysitters that are exchanged interact with the dwarf mongoose exchanging them to gain information about food sources and sleeping mounds, which could result in better-fitted mongooses instead of initializing them afresh as done in DMO, then the counter is reset to zero. The proposed IDMO was used to solve the classical and CEC 2020 benchmark functions and 12 continuous/discrete engineering optimization problems. The performance of the IDMO, using different performance metrics and statistical analysis, is compared with the DMO and eight other existing algorithms. In most cases, the results show that solutions achieved by the IDMO are better than those obtained by the existing algorithms.

关键词： Improved dwarf mongoose Nature-inspired algorithms Constrained optimization Unconstrained optimization Engineering design problems

Scalable Gaussian Process Hyperparameter Optimization via Coverage Regularization

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arXiv 2022年

作者： Wood, Killian Muyskens, Amanda Dunton, Alec M. Priest, Benjamin W. Department of Applied Mathematics University of Colorado Boulder BoulderCO80301 United States Applied Statistics Group Lawrence Livermore National Laboratory LivermoreCA94550 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States

Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction accuracy and uncertainty;uniquely estimating multiple hyperparameters in, e.g. the Matérn kernel can also be a significant challenge. Moreover, training GPs on large-scale datasets is a highly active area of research: traditional maximum likelihood hyperparameter training requires quadratic memory to form the covariance matrix and has cubic training complexity. To address the scalable hyperparameter tuning problem, we present a novel algorithm which estimates the smoothness and length-scale parameters in the Matèrn kernel in order to improve robustness of the resulting prediction uncertainties. Using novel loss functions similar to those in conformal prediction algorithms in the computational framework provided by the hyperparameter estimation algorithm MuyGPs, we achieve improved UQ over leave-one-out likelihood maximization while maintaining a high degree of scalability as demonstrated in numerical *** Codes 60G15 Copyright © 2022, The Authors. All rights reserved.

关键词： Covariance matrix

Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving PDEs with sharp solutions

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arXiv 2023年

作者： Mao, Zhiping Meng, Xuhui School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen China Institute of Interdisciplinary Research for Mathematics and Applied Science School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China

We consider solving the forward and inverse PDEs which have sharp solutions using physics-informed neural networks (PINNs) in this work. In particular, to better capture the sharpness of the solution, we propose adaptive sampling methods (ASMs) based on the residual and the gradient of the solution. We first present a residual only based ASM algorithm denoted by ASM I. In this approach, we first train the neural network by using a small number of residual points and divide the computational domain into a certain number of sub-domains, we then add new residual points in the sub-domain which has the largest mean absolute value of the residual, and those points which have largest absolute values of the residual in this sub-domain will be added as new residual points. We further develop a second type of ASM algorithm (denoted by ASM II) based on both the residual and the gradient of the solution due to the fact that only the residual may be not able to efficiently capture the sharpness of the solution. The procedure of ASM II is almost the same as that of ASM I except that in ASM II, we add new residual points which not only have large residual but also large gradient. To demonstrate the effectiveness of the present methods, we employ both ASM I and ASM II to solve a number of PDEs, including Burger equation, compressible Euler equation, Poisson equation over an L-shape domain as well as high-dimensional Poisson equation. It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASM I or ASM II algorithm, and both methods deliver much more accurate solution than original PINNs with the same number of residual points. Moreover, the ASM II algorithm has better performance in terms of accuracy, efficiency and stability compared with the ASM I algorithm. This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution. Furthermore

关键词： Poisson equation

Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise

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arXiv 2017年

作者： Gunzburger, Max Li, Buyang Wang, Jilu Department of Scientific Computing Florida State University TallahasseeFL32306 United States Department of Applied Mathematics Hong Kong Polytechnic University Hung Hom Hong Kong Department of Mathematics and Statistics Mississippi State University Mississippi State39762 United States

The stochastic time-fractional equation ∂tψ − ∆∂t1−αψ = f + W with space-time white noise W is discretized in time by a backward-Euler convolution quadrature for which the sharp-order error estimate (Ekψ(·, tn) − ψnk2L2(O)) 21 = O(τ 12 − αd 4) is established for α ∈ (0, 2/d), where d denotes the spatial dimension, ψn the approximate solution at the nth time step, and E the expectation operator. In particular, the result indicates sharp convergence rates of numerical solutions for both stochastic subdiffusion and diffusion-wave problems in one spatial dimension. Numerical examples are presented to illustrate the theoretical analysis. Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

Scaling laws and spatial effects of Brazilian health regions: A research protocol

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Scaling laws and spatial effects of Brazilian health regions...

2022 International Conference on ENTERprise Information Systems, CENTERIS 2022 - International Conference on Project MANagement, ProjMAN 2022 and International Conference on Health and Social Care Information Systems and Technologies, HCist 2022

作者： Soares, Giovane Thomazini Yamada, Diego Bettiol Bernardi, Filipe Andrade Neiva, Mariane Barros Lombardi, Luis Pedro Vinci, Andre Luiz Teixeira De Andrade Mioto, Ana Clara Alves, Domingos Ribeirão Preto Medical School University of Sao Paulo Av Bandeirantes 3900SP Ribeirao Preto14049900 Brazil Bioengineering Postgraduate Program Av Trabalhador Sao-Carlense 400SP Sao Carlos13566590 Brazil Institute of Mathematics and Computer Sciences Av Trabalhador Sao-Carlense 400SP Sao Carlos13566590 Brazil Institute of Mathematics Statistics and Scientific Computing State University of Campinas Rua Sergio Buarque de Holanda 651SP Campinas13083859 Brazil

The literature has already consolidated the importance of health regions for Brazilian public health. Complexity properties strongly mark such regions. In this context, there are abundant indications that health regions should be analyzed with approaches linked to the sciences of complexity. One of these approaches, the estimation of scaling laws, can describe important properties of socio-spatial elements. However, no studies estimate the scaling laws of Brazilian health regions. This research protocol can remedy this limitation, proposing the estimation of scaling laws of the previously mentioned regions, mainly considering variables relevant to Brazilian public health. Still, this paper can substantially mitigate other relevant limitations of usual research that estimate scaling laws of socio-spatial elements. These mitigations, which provide advances in the literature on estimating scaling laws, are given by the proposal of modeling (if necessary) spatial effects and estimating scaling laws for the entire population of the socio-spatial elements. According to the theory, the expected results are non-linear scaling laws, which will likely vary with space and time and coexist with relevant spatial effects. From such laws and effects, it will be possible to accurately characterize the performance of each health region through Spatial and Scale Adjusted Metropolitan Indicators and unravel spatio-Temporal properties, stabilities, and instabilities of sets composed of health regions. The expected findings of this paper can help rearrange health regions and improve the quality of information used in Brazilian public health planning. © 2023 Elsevier B.V.. All rights reserved.

关键词： Scaling laws

POINTWISE ESTIMATES FOR THE FUNDAMENTAL SOLUTIONS OF HIGHER ORDER SCHRÖDINGER EQUATIONS IN ODD DIMENSIONS I: LOW DIMENSIONAL CASE

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arXiv 2024年

作者： Cheng, Han Huang, Shanlin Huang, Tianxiao Zheng, Quan Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Sun Yat-sen University Guangdong Zhuhai519082 China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, for any odd n and any integer m ≥ 1 with n tu(x, t) = ((−∆)m + V(x))u(x, t), t ∈ , x ∈ n, where V is a real-valued potential with certain decay. Let Pac(H) denote the projection onto the absolutely continuous spectrum space of H = (−∆)m + V, and assume that H has no positive embedded eigenvalue. Our main result says that e−itHPac(H) has integral kernel K(t, x, y) satisfying (Equation presented), where the constants C, h > 0, and h can be specified by m, n and the zero energy resonances of H. A similar result for smoothing operators like (Equation presented) is also given. One of the main novelties lies in a new and unified approach to obtain the asymptotic expansions of perturbed resolvents under various types of zero energy resonances. © 2024, CC0.

关键词： Schrodinger equation

POINTWISE ESTIMATES FOR THE FUNDAMENTAL SOLUTIONS OF HIGHER ORDER SCHRÖDINGER EQUATIONS IN ODD DIMENSIONS II: HIGH DIMENSIONAL CASE

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arXiv 2024年

In this paper, for any odd n and any integer m ≥ 1 with n > 4m, we study the fundamental solution of the higher order Schrödinger equation i∂tu(x, t) = ((−∆)m + V(x))u(x, t), t ∈ R, x ∈ Rn, where V is a real-valued C n+21 −2m potential with certain decay. Let Pac(H) denote the projection onto the absolutely continuous spectrum space of H = (−∆)m+V, and assume that H has no positive embedded eigenvalue. Our main result says that e−itHPac(H) has integral kernel K(t, x, y) satisfying n(m−1) |K(t, x, y)| ≤ C(1 + |t|)−(2nm −σ)(1 + |t|− 2nm ) (1 + |t|− 21m |x − y|)− 2m−1 , t , 0, x, y ∈ Rn, where σ = 2 if 0 is an eigenvalue of H, and σ = 0 otherwise. A similar result for smoothing operators H 2αm e−itHPac(H) is also given. The regularity condition V ∈ C n+21 −2m is optimal in the second order case, and it also seems optimal when m > 1. © 2024, CC0.

关键词： Schrodinger equation