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Inferring System and Optimal Control Parameters of Closed-Loop Systems from Partial Observations

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arXiv 2025年

作者： Geadah, Victor Arbelaiz, Juncal Ritz, Harrison Daw, Nathaniel D. Cohen, Jonathan D. Pillow, Jonathan W. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ United States Princeton Neuroscience Institute Princeton University PrincetonNJ United States

We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is observed noisily. To recover closed-loop system parameters, we develop inference methods based on probabilistic state-space model (SSM) techniques. First, we show that the system parameters exhibit non-identifiability in the infinite-horizon from closed-loop measurements, and we provide exact and numerical methods to disentangle the parameters. Second, to improve parameter identifiability, we show that we can further enhance recovery by either (1) incorporating additional partial measurements of the control signals or (2) moving to the finite-horizon setting. We further illustrate the performance of our methodology through numerical examples. © 2025, CC BY.

关键词： Stochastic systems

Multirate Time-Integration Based on Dynamic Ode Partitioning Through Adaptively Refined Meshes for Compressible Fluid Dynamics

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SSRN

SSRN 2024年

作者： Doehring, Daniel Schlottke-Lakemper, Michael Gassner, Gregor J. Torrilhon, Manuel Applied and Computational Mathematics RWTH Aachen University Schinkelstrasse 2 North Rhine-Westphalia Aachen52062 Germany University of Stuttgart Germany Department of Mathematics and Computer Science Center for Data and Simulation Science University of Cologne Germany

In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from adaptive mesh refinement. The P-ERK schemes enable multirate time-integration with no changes in the spatial discretization methodology, making them readily implementable in existing codes that employ a method-of- lines *** show that speedup compared to a range of state of the art Runge-Kutta methods can be realized, despite additional overhead due to the dynamic re-assignment of flagging variables and restricting nonlinear stability properties. The effectiveness of the approach is demonstrated for a range of simulation setups for viscous and inviscid convection-dominated compressible flows for which we provide a reproducibility *** addition, we perform a thorough investigation of the nonlinear stability properties of the Paired-Explicit Runge-Kutta schemes regarding limitations due to the violation of monotonicity properties of the underlying spatial discretization. Furthermore, we present a novel approach for estimating the relevant eigenvalues of large Jacobians required for the optimization of stability polynomials . © 2024, The Authors. All rights reserved.

关键词： Runge Kutta methods

Combinatorial Disjunctive Constraints for Obstacle Avoidance in Path Planning

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arXiv 2023年

作者： Garcia, Raul Hicks, Illya V. Huchette, Joey The Department of Computational Applied Mathematics & Operations Research Rice University HoustonTX77005 United States Faculty of Computational Applied Mathematics & Operations Research Rice University HoustonTX77005 United States Google Research CambridgeMA02142 United States

We present a new approach for modeling avoidance constraints in 2D environments, in which waypoints are assigned to obstacle-free polyhedral regions. Constraints of this form are often formulated as mixed-integer programming (MIP) problems employing big-M techniques—however, these are generally not the strongest formulations possible with respect to the MIP’s convex relaxation (so called ideal formulations), potentially resulting in larger computational burden. We instead model obstacle avoidance as combinatorial disjunctive constraints and leverage the independent branching scheme to construct small, ideal formulations. As our approach requires a biclique cover for an associated graph, we exploit the structure of this class of graphs to develop a fast subroutine for obtaining biclique covers in polynomial time. We also contribute an open-source Julia library named ClutteredEnvPathOpt to facilitate computational experiments of MIP formulations for obstacle avoidance. Experiments have shown our formulation is more compact and remains competitive on a number of instances compared with standard big-M techniques, for which solvers possess highly optimized procedures. Copyright © 2023, The Authors. All rights reserved.

关键词： Motion planning

Quasi-Monte Carlo for partial differential equations with generalized Gaussian input uncertainty

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arXiv 2024年

作者： Guth, Philipp A. Kaarnioja, Vesa Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstraße 69 LinzAT-4040 Austria Department of Mathematics and Computer Science Free University of Berlin Arnimallee 6 BerlinDE-14195 Germany

There has been a surge of interest in uncertainty quantification for parametric partial differential equations (PDEs) with Gevrey regular inputs. The Gevrey class contains functions that are infinitely smooth with a growth condition on the higher-order partial derivatives, but which are nonetheless not analytic in general. Recent studies by Chernov and Lê (Comput. Math. Appl., 2024, and SIAM J. Numer. Anal., 2024) as well as Harbrecht, Schmidlin, and Schwab (Math. Models Methods Appl. Sci., 2024) analyze the setting wherein the input random field is assumed to be uniformly bounded with respect to the uncertain parameters. In this paper, we relax this assumption and allow for parameter-dependent bounds. The parametric inputs are modeled as generalized Gaussian random variables, and we analyze the application of quasi-Monte Carlo (QMC) integration to assess the PDE response statistics using randomly shifted rank-1 lattice rules. In addition to the QMC error analysis, we also consider the dimension truncation and finite element errors in this *** Codes 65D30, 65D32, 35R60 Copyright © 2024, The Authors. All rights reserved.

关键词： Monte Carlo methods

Rapid Path Extraction and Three-Dimensional Roaming of the Virtual Endonasal Endoscope

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Chinese Journal of Electronics 2021年第3期30卷 397-405页

作者： WANG Yudong HAN Jing PAN Junjun WANG Jing CAO Yi ZHU Li LUO Yanlin School of Artificial Intelligence Beijing Normal University State Key Laboratory of Virtual Reality Technology and Systems Beihang University Institute of Applied Physics and Computational Mathematics Department of Otolaryngology Head and Neck Surgery Peking University Third Hospital

Compared with traditional endonasal endoscope, Virtual endonasal endoscope(VEE) is a computerized alternative solution with the advantages of being non-invasive, affordable, no perforation, low risk of infection, and high degree of sensitivity. A Central path extraction algorithm based on Pre-planning of the roaming area(CPE-PRA) is proposed to extract the central path of the nasal cavity model efficiently. And a B-spline curve fitting algorithm based on Relative center deviation(RCD)is introduced to fit a smooth curve to the extracted path,so that the virtual camera could have both a steady turning speed and a broad vision. A series of comparison tests were conducted to evaluate the effectiveness and efficiency of the proposed algorithms.

关键词： virtual instrumentation Virtual endonasal endoscope RCD rapid path extraction nasal cavity model medical image processing VEE feature extraction path planning CPE-PRA splines (mathematics) B-spline curve fitting algorithm computerized alternative solution roaming area relative center deviation virtual camera Central path extraction algorithm curve fitting endoscopes surgery medical robotics three-dimensional roaming

Return prediction for healthcare sector stocks by using Long Short-Term Memory Algorithm

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Return prediction for healthcare sector stocks by using Long...

2022 International Conference on Cyber Security, Artificial Intelligence, and Digital Economy, CSAIDE 2022

作者： Chen, Zeyi Liu, Chengyuan Wo, Eran Business School Tulane University New Orleans United States Applied & Computational Mathematical Science University of Washington Seattle United States Mathematics and Statistic Department University of Victoria Victoria Canada

ISBN: (纸本)9781510657304

The research is conducted during the rage of COVID-19 throughout the world. The world meets new challenges from COVID-19 from every dimension, especially the economical world. In the economic world, the most related part for the influence that springs from COVID-19 is the stocks belonging to the healthcare sector. Aiming at doing the return prediction for healthcare sector stocks, the study chooses Long Short-Term Memory (LSTM) Algorithm to introduce machines to adapt the pattern and make predictions. The study selects 6 less volatile while keeping high average trading volume stocks from the healthcare sector. Using the LSTM learning model to learn the past 5 years’ data and make the prediction to the future 5 days. The data consist of 65% of the company's data from five years ago as the training set, and the last 35% of the data as the test set. The study compares the actual data to the predicted data and sees the error by calculating root mean square error (RMSE). The result draws the conclusion that the model will perform more precise prediction when the picked stock has a clear price trend and less fluctuation. The application for this study is to provide a short-term trading strategy and manage the risk for short-term stock investment by using the LSTM model. © 2022 SPIE.

关键词： Long short-term memory

A Unified Approach to Inferring Chemical Compounds with the Desired Aqueous Solubility

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arXiv 2024年

作者： Batool, Muniba Azam, Naveed Ahmed Zhu, Jianshen Haraguchi, Kazuya Zhao, Liang Akutsu, Tatsuya Discrete Mathematics and Computational Intelligence Laboratory Department of Mathematics Quaid-i-Azam University Pakistan Discrete Mathematics Laboratory Department of Applied Mathematics and Physics Graduate School of Informatics Kyoto University Kyoto606-8501 Japan Kyoto University Kyoto606-8306 Japan Bioinformatics Center Institute for Chemical Research Kyoto University Uji611-0011 Japan

Aqueous solubility (AS) is a key physiochemical property that plays a crucial role in drug discovery and material design. We report a novel unified approach to predict and infer chemical compounds with the desired AS based on simple deterministic graph-theoretic descriptors, multiple linear regression (MLR) and mixed integer linear programming (MILP). Selected descriptors based on a forward stepwise procedure enabled the simplest regression model, MLR, to achieve significantly good prediction accuracy compared to the existing approaches, achieving the accuracy in the range [0.7191, 0.9377] for 29 diverse datasets. By simulating these descriptors and learning models as MILPs, we inferred mathematically exact and optimal compounds with the desired AS, prescribed structures, and up to 50 non-hydrogen atoms in a reasonable time range [6, 1204] seconds. These findings indicate a strong correlation between the simple graph-theoretic descriptors and the AS of compounds, potentially leading to a deeper understanding of their AS without relying on widely used complicated chemical descriptors and complex machine learning models that are computationally expensive, and therefore difficult to use for inference. An implementation of the proposed approach is available at https://***/ku-dml/mol-infer/tree/master/AqSol. © 2024, CC BY.

关键词： Solubility

Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative

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arXiv 2024年

作者： Zinihi, Achraf Ammi, Moulay Rchid Sidi Ehrhardt, Matthias Department of Mathematics MAIS Laboratory AMNEA Group Faculty of Sciences and Technics Moulay Ismail University of Meknes Errachidia52000 Morocco University of Wuppertal Chair of Applied and Computational Mathematics Gaußstrasse 20 Wuppertal42119 Germany

In this work we study a fractional SEIR biological model of a reaction-diffusion, using the non-singular kernel Caputo-Fabrizio fractional derivative in the Caputo sense and employing the Laplacian operator. In our PDE model, the government seeks immunity through the vaccination program, which is considered a control variable. Our study aims to identify the ideal control pair that reduces the number of infected/infectious people and the associated vaccine and treatment costs over a limited time and space. Moreover, by using the forward-backward algorithm, the approximate results are explained by dynamic graphs to monitor the effectiveness of *** Codes 92C60, 26A33, 34K08, 33F05, 49J20 © 2024, CC BY.

关键词： Vaccines

Gaussian Interpolation Flows

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arXiv 2023年

作者： Gao, Yuan Huang, Jian Jiao, Yuling Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong Departments of Data Science and AI and Applied Mathematics The Hong Kong Polytechnic University Hong Kong School of Mathematics and Statistics Hubei Key Laboratory of Computational Science Wuhan University Wuhan China

Gaussian denoising has emerged as a powerful method for constructing simulation-free continuous normalizing flows for generative modeling. Despite their empirical successes, theoretical properties of these flows and the regularizing effect of Gaussian denoising have remained largely unexplored. In this work, we aim to address this gap by investigating the well-posedness of simulation-free continuous normalizing flows built on Gaussian denoising. Through a unified framework termed Gaussian interpolation flow, we establish the Lipschitz regularity of the flow velocity field, the existence and uniqueness of the flow, and the Lipschitz continuity of the flow map and the time-reversed flow map for several rich classes of target distributions. This analysis also sheds light on the auto-encoding and cycle consistency properties of Gaussian interpolation flows. Additionally, we study the stability of these flows in source distributions and perturbations of the velocity field, using the quadratic Wasserstein distance as a metric. Our findings offer valuable insights into the learning techniques employed in Gaussian interpolation flows for generative modeling, providing a solid theoretical foundation for end-to-end error analyses of learning Gaussian interpolation flows with empirical *** Codes 62G05, 68T07 © 2023, CC BY.

关键词： Stochastic systems