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A folding preprocess for the max k-cut problem

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Optimization Letters 2025年第5期19卷 899-917页

作者： Fakhimi, Ramin Validi, Hamidreza Hicks, Illya V. Terlaky, Tamás Zuluaga, Luis F. Department of Industrial and Systems Engineering Lehigh University Bethlehem United States Department of Industrial Manufacturing & Systems Engineering Texas Tech University Lubbock United States Department of Computational Applied Mathematics & Operations Research Rice University Houston United States

Given graph G=(V,E) with vertex set V and edge set E, the max k-cut problem seeks to partition the vertex set V into at most k subsets that maximize the weight (number) of edges with endpoints in different parts. This paper proposes a graph folding procedure (i.e., a procedure that reduces the number of the vertices and edges of graph G) for the weighted max k-cut problem that may help reduce the problem’s dimensionality. While our theoretical results hold for any k≥2, our computational results show the effectiveness of the proposed preprocess only for k=2 and on two sets of instances. Furthermore, we observe that the preprocess improves the performance of a MIP solver on a set of large-scale instances of the max cut problem. © The Author(s) 2025.

关键词： Network theory (graphs)

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

Unbiased Parameter Estimation for Bayesian Inverse Problems

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China 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

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

Periodic propagation of singularities for heat equations with time delay

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arXiv 2025年

作者： Wang, Gengsheng Yu, Huaiqiang Zhang, Yubiao Center for Applied Mathematics KL-AAGDM Tianjin University Tianjin300072 China School of Mathematics KL-AAGDM Tianjin University Tianjin300350 China Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstraße 69 Upper Austria Linz4040 Austria Chair for Dynamics Control Machine Learning and Numerics Department of Mathematics Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen91058 Germany

This paper presents two remarkable phenomena associated with the heat equation with a time delay: namely, the propagation of singularities and periodicity. These are manifested through a distinctive mode of propagation of singularities in the solutions. Precisely, the singularities of the solutions propagate periodically in a bidirectional fashion along the time axis. Furthermore, this propagation occurs in a stepwise manner. More specifically, when propagating in the positive time direction, the order of the joint derivatives of the solution increases by 2 for each period;conversely, when propagating in the reverse time direction, the order of the joint derivatives decreases by 2 per period. Additionally, we elucidate the way in which the initial data and historical values impact such a propagation of singularities. The phenomena we have discerned not only corroborate the pronounced differences between heat equations with and without time delay but also vividly illustrate the substantial divergence between the heat equation with a time delay and the wave equation, especially when viewed from the point of view of singularity *** Codes 35K05 45K05 58J47 © 2025, CC BY.

关键词： Wave equations

SPECIAL ORTHOGONAL, SPECIAL UNITARY, AND SYMPLECTIC GROUPS AS PRODUCTS OF GRASSMANNIANS

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arXiv 2025年

作者： Lim, Lek-Heng Lu, Xiang Ye, Ke Computational and Applied Mathematics Initiative University of Chicago ChicagoIL60637 United States Department of Statistics University of Chicago ChicagoIL60637 United States KLMM Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of their corresponding Grassmannians realized as involution matrices. We will show that SO(n) is a product of two real Grassmannians, SU(n) a product of four complex Grassmannians, and Sp(2n, R) or Sp(2n, C) a product of four symplectic Grassmannians over or ℂ *** Codes 14M15, 22E10, 22E15, 51A50 © 2025, CC BY.

关键词： Matrix algebra

Advancements on multi-fidelity random Fourier neural networks: application to hurricane modeling for offshore wind energy

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Advancements on multi-fidelity random Fourier neural network...

AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2025

作者： Davis, Owen Geraci, Gianluca Wentz, Jacqueline M. King, Ryan N. Cortiella, Alexandre Rybchuk, Alex Gomez, Miguel Sanchez Deskos, Georgios Motamed, Mohammad Optimization and Uncertainty Quantification Sandia National Laboratories AlbuquerqueNM United States Computational Data Science Sandia National Laboratories LivermoreCA United States National Wind Technology Center National Renewable Energy Laboratory GoldenCO United States Department of Applied Mathematics and Statistics University of New Mexico AlbuquerqueNM United States

ISBN: (数字)9781624107238

ISBN: (纸本)9781624107238

Multi-fidelity approaches are emerging as effective strategies in computational science to handle otherwise intractable tasks like Uncertainty Quantification (UQ), training of Machine Learning (ML) models, and optimization, for expensive high-fidelity applications in which the amount of available simulations or data is limited. The main idea is simple: large datasets generated for low-fidelity approximations of the problem at hand are fused with a much sparser dataset for the target (high-fidelity) system. In this paper, we build on our recent success in designing random Fourier Neural Networks (rFNNs) [1] to target problems arising in wind energy applications and in particular problems of interest for hurricane modeling. In this context, data for the high-fidelity models are limited and lower fidelity alternatives are needed. In this work, we introduce a novel multi-fidelity training approach for our rFNNs and demonstrate its use on a simple verification problem and on a hurricane modeling problem in which high-fidelity data are generated via Large-Eddy Simulations (LES), while low-fidelity data are given by a mesoscale model. Initial results demonstrate how the multi-fidelity training approach can improve the quality of the resulting surrogate. © 2025, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

关键词： Large eddy simulation

FLUID-STRUCTURE INTERACTION WITH POROUS MEDIA: THE BEAVER-JOSEPH CONDITION IN THE STRONG SENSE

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arXiv 2025年

作者： Binz, Tim Hieber, Matthias Roy, Arnab Princeton University Program in Applied & Computational Mathematics Fine Hall Washington Road PrincetonNJ08544 United States Technische Universität Darmstadt Schloßgartenstraße 7 Darmstadt64289 Germany

This article considers fluid structure interaction describing the motion of a fluid contained in a porous medium. The fluid is modelled by Navier-Stokes equations and the coupling between fluid and the porous medium is described by the classical Beaver-Joseph or the Beaver-Joseph-Saffman interface condition. In contrast to previous work these conditions are investigated for the first time in the strong sense and it is shown that the coupled system admits a unique, global strong solution in critical spaces provided the data are small enough. Furthermore, a Serrin-type blow-up criterium is developed and higher regularity estimates at the interface are established, which say that the solution is even analytic provided the forces are so. Copyright © 2025, The Authors. All rights reserved.

关键词： Navier Stokes equations

A One Dimensional (1D) computational Fluid Dynamics Study of Fontan-Associated Liver Disease (FALD)

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arXiv 2025年

作者： Li, Yaqi Puelz, Charles Olufsen, Mette S. Taylor-Lapole, Alyssa Department of Brain and Cognitive Sciences Massachusetts Institute of Technology CambridgeMA02139 United States Mathematics University of Houston HoustonTX77204 United States Department of Mathematics North Carolina State University RaleighNC27695 United States Computational Applied Mathematics and Operations Research Rice University HoustonTX77251 United States

Fontan-Associated Liver Disease (FALD) is a disorder arising from hemodynamic changes and venous congestion in the liver. This disease is prominent in patients with hypoplastic left heart syndrome (HLHS). Although HLHS patients typically survive into adulthood, they have reduced cardiac output due to their univentricular physiology (i.e., a Fontan circuit). As a result, they have insufficient blood delivery to the liver. In comparison, patients with double outlet right ventricle (DORV), also having a univentricular circuit, have lower incidence of FALD. In this study, we use a patient-specific, one-dimensional computational fluid dynamics (1D-CFD) model to predict hemodynamics in the liver of an HLHS patient and compare predictions with an age- and size-matched DORV control patient. Additionally, we simulate FALD conditions in the HLHS patient to predict hemodynamic changes across various stages of disease progression. Our results show that the HLHS patient has a higher portal venous pressure compared to the DORV patient. This difference is exacerbated as FALD conditions progress. The wall shear stress (WSS) is also higher than normal for the HLHS patient, suggesting vascular remodeling. WSS decreases slightly under FALD conditions, consistent with the development of portal hypertension. Perfusion analysis gives insight into regions of liver tissue at risk for fibrosis development, showing increasing pressures and reduced flow throughout the liver tissue fed by the portal vein under FALD conditions. Our results provide insight into the specific hemodynamic changes in Fontan circulation that can cause FALD. © 2025, CC BY.

关键词： Shear stress

Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator

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Statistics and Probability Letters 2025年 223卷

作者： Li, Yizhou Polak, Paweł Department of Applied Mathematics and Statistics Stony Brook University United States Institute for Advanced Computational Science Stony Brook University United States

We show weak convergence of the empirical Conditional Value-at-Risk (CVaR) in functional space and the asymptotic normality of the CVaR-based Pickands estimator from Chen (2021). These results demonstrate that the CVaR-based estimator has significantly lower asymptotic variance than analogous VaR-based constructions. © 2025 Elsevier B.V.

关键词： Asymptotic normality Conditional Value-at-Risk Extreme value index Pickands estimator Second-order regular variation