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Using LDLT factorizations in Newton's method for solving general large-scale algebraic Riccati equations

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arXiv 2024年

作者： Saak, Jens Werner, Steffen W.R. Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstraße 1 Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be computed to all possible formulations of the Riccati equation. This is not the case when it comes to large-scale sparse coefficient matrices. In this paper, we provide a reformulation of the Newton-Kleinman iteration scheme for continuous-time algebraic Riccati equations using indefinite symmetric low-rank factorizations. This allows the application of the method to the case of general large-scale sparse coefficient matrices. We provide convergence results for several prominent realizations of the equation and show in numerical examples the effectiveness of the *** Codes 15A24, 49M15, 65F45, 65H10, 93A15 Copyright © 2024, The Authors. All rights reserved.

关键词： Continuous time systems

Empirical sparse regression on quadratic manifolds-

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arXiv 2024年

作者： Schwerdtner, Paul Gugercin, Serkan Peherstorfer, Benjamin Courant Institute of Mathematical Sciences New York University New YorkNY10012 United States Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation spaces, limiting their effectiveness for data representing transport-dominated and wave-like dynamics. To address this limitation, we introduce quadratic manifold sparse regression, which trains quadratic manifolds with a sparse greedy method and computes approximations on the manifold through novel nonlinear projections of sparse samples. The nonlinear approximations obtained with quadratic manifold sparse regression achieve orders of magnitude higher accuracies than linear methods on data describing transport-dominated dynamics in numerical *** Codes 65F55, 62H25, 65F30, 68T09, 65F20, 65M22 Copyright © 2024, The Authors. All rights reserved.

关键词： Nonlinear simulations

Multilevel Particle Filters for Partially Observed McKean-Vlasov Stochastic Differential Equations

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arXiv 2024年

作者： Awadelkarim, Elsiddig 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 School of Data Science The Chinese University of Hong Kong Shenzhen China

In this paper we consider the filtering problem associated to partially observed McKean-Vlasov stochastic differential equations (SDEs). The model consists of data that are observed at regular and discrete times and the objective is to compute the conditional expectation of (functionals) of the solutions of the SDE at the current time. This problem, even the ordinary SDE case is challenging and requires numerical approximations. Based upon the ideas in [3, 12] we develop a new particle filter (PF) and multilevel particle filter (MLPF) to approximate the afore-mentioned expectations. We prove under assumptions that, for ϵ > 0, to obtain a mean square error of O(ϵ2) the PF has a cost per-observation time of O(ϵ−5) and the MLPF costs O(ϵ−4) (best case) or O(ϵ−4 log(ϵ)2) (worst case). Our theoretical results are supported by numerical experiments. © 2024, CC BY.

关键词： Mean square error

Scheme and Construction of a Smart Vacuum Cleaner Robot 3

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Scheme and Construction of a Smart Vacuum Cleaner Robot

3rd International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies, ICAECT 2023

作者： Hasan, Md. Ibrahim Zeyad, Mohammad Ahmed, S.M. Masum Tasrif Anubhove, Md. Sadik Hossain, Eftakhar Hasan, Sayeed Mahmud, Dewan Mahnaaz Advanced Bioinformatics Computational Biology and Data Science Laboratory Bangladesh Energy and Technology Research Division Chattogram4226 Bangladesh Erasmus+ Joint MSC in Smart Cities and Communities Heriot-Watt University Edinburgh United Kingdom Erasmus+ Joint MSC in Smart Cities and Communities Faculty of Engineering Mons Belgium

ISBN: (纸本)9781665494007

A smart vacuum robot is a remarkable technological achievement that makes cleaning more efficient, faster, and easier. According to this study, the smart vacuum cleaning robot can be operated manually, automatically, mopped/swept, vacuumed/vacuumed, and observed from 360°. A design of a smart vacuum-cleaning robot is proposed with different characteristics. The Arduino IDE and Proteus Design Suite 8 Professional software were employed for analytical analysis, with a microcontroller serving as the primary control component. The hardware implementation comprises a microcontroller, ultrasonic sensor, and light-dependent resistor (LDR) where the ultrasonic sensor identifies obstacles (trash). Therefore, the LDR emits light and sends the microcontroller's signal to the microprocessor. All the sensors in the proposed system operated flawlessly during the experiment. Moreover, all the sensors were performing perfectly. With additional features of this robot, it can continue its operation during darkness. The proposed robot is equipped with a number of creative and intelligent features that allow it to provide the maximum possible support to employees, housewives, and ordinary people. This work presents a new notion of an advanced cleaning robot employing cutting-edge technology that can work independently in automated and regular situations and dramatically improve the cleaning system for humanity. © 2023 IEEE.

关键词： Microcontrollers

FinML-Chain: A Blockchain-Integrated dataset for Enhanced Financial Machine Learning

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arXiv 2024年

作者： Chen, Jingfeng Deng, Wanlin Chen, Dangxing Zhang, Luyao Data Science Research Center Social Science Division United States Zu Chongzhi Center for Mathematics and Computational Sciences China Duke Kunshan University Duke Avenue No.8 Kunshan Suzhou Jiangsu215316 China

Machine learning has become essential for innovation and efficiency in financial markets, offering predictive models and data-driven decision-making. However, challenges such as missing data, lack of transparency, untimely updates, insecurity, and incompatible data sources hinder its effectiveness. These limitations reduce the accuracy and reliability of predictive models. Blockchain technology, with its transparency, immutability, and real-time updates, offers solutions to these challenges. In this paper, we introduce not just a dataset but a new framework for integrating high-frequency on-chain data with low-frequency off-chain data, providing a benchmark for addressing novel research questions in economic mechanism design. This framework enables the generation of modular, extensible datasets tailored to advancing the analysis of economic mechanisms such as the Transaction Fee Mechanism, facilitating multi-modal insights and fairness-driven evaluations. Through time series analysis using four machine learning techniques—linear regression, deep neural networks, XGBoost, and LSTM models—we demonstrate the framework’s capability to produce datasets that drive innovation in financial research and enhance the understanding of blockchain-driven economic systems. Our contributions are threefold: first, we propose a novel research scenario for the Transaction Fee Mechanism and demonstrate how our framework can address previously unexplored questions in economic mechanism design. Second, we provide a new benchmark for financial machine learning by open-sourcing both the sample dataset generated by our framework and the code for the pipeline, allowing future researchers to append new data and expand the datasets continuously. Third, by ensuring that the framework and its outputs are fully open-source, we promote reproducibility, transparency, and collaboration within the research community. This initiative enables researchers to extend our work, tackle a broader range of ec

关键词： Deep neural networks

KLAP: KYP LEMMA BASED LOW-RANK APPROXIMATION FOR H2-OPTIMAL PASSIVATION

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arXiv 2025年

作者： Nicodemus, Jonas Voigt, Matthias Gugercin, Serkan Unger, Benjamin University of Stuttgart Universitätsstr. 32 Stuttgart70569 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States Faculty of Mathematics and Computer Science UniDistance Suisse Schinerstr. 18 Brig3900 Switzerland

We present a novel passivity enforcement (passivation) method, called KLAP, for linear time-invariant systems based on the Kalman-Yakubovich-Popov (KYP) lemma and the closely related Lur’e equations. The passivation problem in our framework corresponds to finding a perturbation to a given non-passive system that renders the system passive while minimizing the H2 or frequency-weighted H2 distance between the original non-passive and the resulting passive system. We show that this problem can be formulated as an unconstrained optimization problem whose objective function can be differentiated efficiently even in large-scale settings. We show that any minimizer of the unconstrained problem yields the same passive system. Furthermore, we prove that, in the absence of a feedthrough term, every local minimizer is also a global minimizer. For cases involving a non-trivial feedthrough term, we analyze global minimizers in relation to the extremal solutions of the Lur’e equations, which can serve as tools for identifying local minima. To solve the resulting numerical optimization problem efficiently, we propose an initialization strategy based on modifying the feedthrough term and a restart strategy when it is likely that the optimization has converged to a local minimum. Numerical examples illustrate the effectiveness of the proposed *** Codes 37J06, 37M99, 65P10, 93A30, 93B30, 93C05 © 2025, CC BY.

关键词： Convergence of numerical methods

Balanced truncation with conformal maps

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arXiv 2024年

作者： Borghi, Alessandro Breiten, Tobias Gugercin, Serkan Technical University of Berlin Mathematics Department Straße des 17. Juni 136 Berlin10623 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

We consider the problem of constructing reduced models for large scale systems with poles in general domains in the complex plane (as opposed to, e.g., the open left-half plane or the open unit disk). Our goal is to design a model reduction scheme, building upon theoretically established methodologies, yet encompassing this new class of models. To this aim, we develop a balanced truncation framework through conformal maps to handle poles in general domains. The major difference from classical balanced truncation resides in the formulation of the Gramians. We show that these new Gramians can still be computed by solving modified Lyapunov equations for specific conformal maps. A numerical algorithm to perform balanced truncation with conformal maps is developed and is tested on three numerical examples, namely a heat model, the Schrödinger equation, and the undamped linear wave equation, the latter two having spectra on the imaginary axis. Copyright © 2024, The Authors. All rights reserved.

关键词： Poles

FREQUENCY-BASED REDUCED MODELS FROM PURELY TIME-DOMAIN data VIA data INFORMATIVITY

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arXiv 2023年

作者： Ackermann, Michael S. Gugercin, Serkan Department of Mathematics Virginia Tech BlacksburgVA24061 United States Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Frequency-based methods have been successfully employed in creating high-fidelity data-driven reduced order models (DDROMs) for linear dynamical systems. These methods require access to values (and sometimes derivatives) of the frequency-response function (transfer function) in the complex plane. These frequency domain values can at times be costly or difficult to obtain (especially if the method of choice requires resampling);instead one may have access to only time-domain input-output data. The data informativity approach to moment matching provides a powerful new framework for recovering the required frequency data from a single time-domain trajectory. In this work, we analyze and extend upon this framework, resulting in significantly improved conditioning of the associated linear systems, an error indicator, and the removal of an assumption that the system order is known. This analysis leads to a robust algorithm for recovering frequency information from time-domain data, suitable for large-scale systems. We demonstrate the effectiveness of our algorithm by forming frequency-based DDROMs from time-domain data of several dynamical systems. Copyright © 2023, The Authors. All rights reserved.

关键词： Transfer functions

Optimal Design of Color Laparoscopic Super-Resolution Image Quality Based on Generative Adversarial Networks

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Optimal Design of Color Laparoscopic Super-Resolution Image ...

Computer Graphics and Image Processing (CGIP), International Conference on

作者： Norifumi Kawabata Toshiya Nakaguchi Education and Research Center for Mathematical and Data Science Hokkaido University Sapporo Japan Research Division of Computational Imaging Computational Imaging Lab Sapporo Japan Center for Frontier Medical Engineering Chiba University Chiba Japan

The Generative Adversarial Networks (GAN) is unsupervised learning enabled to transform according to data characteristics, though this generate unreal data by learning characteristics from data. As past our study, we discussed from the viewpoint of image quality for super-resolution of color laparoscopic image including SRCNN (Super-Resolution Convolutional Neural Network). However, it was not enough to compare to other neural network methods in our discussion. We consider that it is possible to support the medical image diagnosis by measuring whether the difference of both neural network method and image contents is affected or not for image quality. In this paper, first we carried out the objective image quality assessment by designing optimally of color laparoscopic super-resolution image using Generative Adversarial Networks (GAN). And then, we discussed for performance between methods comparing to result of SRCNN. On the other hand, from a view of information science, we consider that we need to verify experimentally for affect between network learning effect and generated image, and then to improve method. Therefore, we also discussed relationship between image quality and learning effect in color laparoscopic image generation using SRGAN.

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