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Optimal Estimation in Spatially Distributed Systems: How Far to Share Measurements From?

IEEE Transactions on Automatic Control 2025年第5期70卷 3226-3239页

作者： Arbelaiz, Juncal Bamieh, Bassam Hosoi, Anette E. Jadbabaie, Ali Massachusetts Institute of Technology Department of Applied Mathematics CambridgeMA02139 United States Princeton University Center for Statistics and Machine Learning PrincetonNJ08542 United States University of California Department of Mechanical Engineering Santa BarbaraCA93106 United States Massachusetts Institute of Technology Department of Mechanical Engineering CambridgeMA02139 United States Massachusetts Institute of Technology Department of Civil and Environmental Engineering Institute for Data Systems and Society CambridgeMA02139 United States

In this article, we consider the centralized optimal estimation problem in spatially distributed systems. We use the setting of spatially invariant systems as an idealization for which concrete and detailed results are given. Such estimators are known to have a degree of spatial localization in the sense that the estimator gains decay in space, with the spatial decay rates serving as a proxy for how far measurements need to be shared in an optimal distributed estimator. In particular, we examine the dependence of spatial decay rates on problem specifications such as system dynamics, measurement, and process noise variances, as well as their spatial autocorrelations. We propose nondimensional parameters that characterize the decay rates as a function of problem specifications. In particular, we find an interesting matching condition between the characteristic lengthscale of the dynamics and the measurement noise correlation lengthscale for which the optimal centralized estimator is completely decentralized. A new graphical technique—termed the branch point locus—is introduced to quantify spatial decay rates in terms of analyticity regions in the complex spatial frequency plane. Our results are illustrated through two case studies of systems with dynamics modeled by diffusion and the Swift–Hohenberg equation, respectively. © 1963-2012 IEEE.

关键词： Uncertain systems

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Critically-Damped Third-Order Langevin Dynamics

Critically-Damped Third-Order Langevin Dynamics

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Benjamin Sterling Mónica F. Bugallo Department of Applied Math & Statistics Stony Brook University Stony Brook NY USA Department of Electrical and Computer Engineering Stony Brook University Stony Brook NY USA

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

While systems analysis has been studied for decades in the context of control theory, it has only been recently used to improve the convergence of Denoising Diffusion Probabilistic Models. This work describes a novel improvement to Third-Order Langevin Dynamics (TOLD), a recent diffusion method that performs better than its predecessors. This improvement, abbreviated TOLD++, is carried out by critically damping the TOLD forward transition matrix similarly to Dockhorn’s Critically-Damped Langevin Dynamics (CLD). Specifically, it exploits eigen-analysis of the forward transition matrix to derive the optimal set of dynamics under the original TOLD scheme. TOLD++ is theoretically guaranteed to converge faster than TOLD, and its faster convergence is verified on the Swiss Roll toy dataset and CIFAR-10 dataset according to the FID metric.

关键词： Damping Measurement Training Toy manufacturing industry Noise reduction Signal processing Diffusion models Speech processing System analysis and design Convergence

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The origin of vorticity in viscous incompressible flows

arXiv

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arXiv 2025年

作者： Xiang, Tianrui Eyink, Gregory L. Zaki, Tamer A. Department of Mechanical Engineering Johns Hopkins University BaltimoreMD21218 United States Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States

In inviscid, incompressible flows, the evolution of vorticity is exactly equivalent to that of an infinitesimal material line-element, and hence vorticity can be traced forward or backward in time in a Lagrangian fashion. This elegant and powerful description is not possible in viscous flows due to the action of diffusion. Instead, a stochastic Lagrangian interpretation is required and was recently introduced, where the origin of vorticity at a point is traced back in time as an expectation over the contribution from stochastic trajectories. We herein introduce for the first time an Eulerian, adjoint-based approach to quantify the back-in-time origin of vorticity in viscous, incompressible flows. The adjoint variable encodes the advection, tilting and stretching of the earlier-in-time vorticity that ultimately leads to the target value. Precisely, the adjoint vorticity is the volume-density of the mean Lagrangian deformation of the earlier vorticity. The formulation can also account for the injection of vorticity into the domain at solid boundaries. We demonstrate the mathematical equivalence of the adjoint approach and the stochastic Lagrangian approach. We then provide an example from turbulent channel flow, where we analyze the origin of high-stress events and relate them to Lighthill’s mechanism of stretching of near-wall vorticity. © 2025, CC BY.

关键词： Stochastic systems

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Josephson-Anderson relation as diagnostic of turbulent drag reduction by polymers

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Physical Review E 2025年第1期111卷 015105-015105页

作者： Samvit Kumar Simon Toedtli Tamer A. Zaki Gregory L. Eyink Department of Applied Mathematics & Statistics Johns Hopkins University Baltimore Maryland 21218 USA Department of Mechanical Engineering Johns Hopkins University Baltimore Maryland 21218 USA Department of Physics & Astronomy The Johns Hopkins University Baltimore Maryland 21218 USA

The detailed Josephson-Anderson relation, which equates instantaneously the volume-integrated vorticity flux and the work by pressure drop, has been the key to drag reduction in superconductors and superfluids. We employ a classical version of this relation to investigate the dynamics of polymer drag-reduced channel flows, particularly in the high-extent drag reduction (HDR) regime which is known to exhibit strong space-time intermittency. We show that high drag is not created instantaneously by near-wall coherent vortex structures as assumed in prior works. These predominantly spanwise near-wall vortex structures can produce a net “up-gradient” flux of vorticity toward the wall, which instead reduces instantaneous drag. Increase of wall vorticity and skin friction due to this up-gradient flux occurs after an apparent lag of several advection times, increasing with the Weissenberg number. This increasing lag appears to be due to polymer damping of up-gradient nonlinear vorticity transport that arises from large-scale eddies in the logarithmic layer. The relatively greater polymer damping of down-gradient transport due to small-scale eddies results in lower net vorticity flux and hence lower drag. The Josephson-Anderson relation thus provides an exact tool to diagnose the mechanism of polymer drag reduction in terms of vorticity dynamics and it explains also prior puzzling observations on transient drag reduction, as for centerline-release experiments in pipe flow.

关键词： Vorticity

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A local meshfree approach based on compactly supported radial basis functions for 2D coupled fluid dynamics PDEs on regular and irregular domains

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engineering Analysis with Boundary Elements 2025年 177卷

作者： Keita, Lanceni Azrar, Lahcen Al-Ghamedi, Ateq Ahmed Research Center STIS M2CS Department of Applied Mathematics and Informatics ENSAM Mohammed V University Rabat Morocco Faculty of Engineering Department of Mechanical Engineering King Abdulaziz University Jeddah Saudi Arabia Faculty of Sciences Department of statistics King Abdulaziz University Jeddah Saudi Arabia

This paper presents a novel application of compactly supported radial basis functions (CSRBFs) within a local meshfree framework to solve two-dimensional coupled partial differential equations, including the Burgers’ equation (2D-CVBE) and the Saint Venant system (2D-SVS), also known as the shallow water equations. By integrating CSRBFs with the method of lines (CSRBF-MOL), this approach provides a flexible and adaptive meshfree discretization technique. It reformulates the 2D-CVBE and 2D-SVS into systems of ordinary differential equations, which are then solved numerically. The proposed method has capability to handle both rectangular and irregular domains without requiring structured grids. Its compatibility to deal with Neumann boundary conditions in makes it particularly effective for complex geometries. This framework offers a robust alternative for fluid dynamics simulations, addressing the limitations of traditional mesh-based methods in terms of flexibility and computational efficiency. The method's accuracy and reliability are demonstrated through six numerical experiments, with results compared to global RBF approaches and conventional mesh-based techniques from the current literature. © 2025 Elsevier Ltd

关键词： Ordinary differential equations

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Geometry-Driven Design of Morphable Surface Structures Using Topology Optimization and Circle Packing

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Journal of mechanical Design 2025年第9期147卷 091701页

作者： Gao, Lingfeng Zhu, Xiaoping Tanaka, Masato Song, Yuyang Zhou, Yuqing Gu, Xianfeng David Chen, Shikui Department of Mechanical Engineering https://***/05qghxh33State University of New York at Stony Brook Stony Brook NY 11794 Department of Applied Mathematics & Statistics https://***/05qghxh33State University of New York at Stony Brook Stony Brook NY 11794 Toyota Research Institute of North America Ann Arbor MI 48105 Department of Computer Science Department of Applied Mathematics & Statistics State University of New York at Stony Brook Stony Brook NY 11794 Department of Mechanical Engineering State University of New York at Stony Brook Stony Brook NY 11794

This paper introduces a new computational framework for modeling and designing morphable surface structures based on an integrated approach that leverages circle packing for surface representation, conformal mapping to link local and global kinematics, and topology optimization for actuator design. The framework utilizes a unique strategy for employing optimized compliant actuators as the basic building blocks of the morphable surface. These actuators, designed as circular elements capable of modifying their radius and curvature, are optimized using level set topology optimization, considering both kinematic performance and structural stiffness. Circle packing is employed to represent the surface geometry, while conformal mapping guides the kinematic analysis, ensuring alignment between local actuator motions and desired global surface transformations. The design process involves mapping optimized component designs back onto the circle packing representation, facilitating coordinated control, and achieving harmony between local and global geometries. This leads to efficient actuation and enables precise control over the surface morphology. The effectiveness of the proposed framework is demonstrated through two numerical examples, showcasing its capability to design complex, morphable surfaces with potential applications in fields requiring dynamic shape adaptation.

关键词： Geometry Design circle packing computer-aided engineering Packings (Cushioning) compliant mechanisms topology optimization morphable structures level set method Packing (Shipments) conformal mapping Shapes conceptual design Actuators simulation-based design computational geometry Topology optimization differential geometry

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A Statistical Framework for District Energy Long-term Electric Load Forecasting

arXiv

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arXiv 2025年

作者： Royal, Emily Bandyopadhyay, Soutir Newman, Alexandra Huang, Qiuhua Tabares-Velasco, Paulo Cesar Colorado School of Mines Department of Electrical Engineering 1500 Illinois Street GoldenCO80401 United States Colorado School of Mines Department of Applied Mathematics and Statistics 1500 Illinois Street GoldenCO80401 United States Colorado School of Mines Department of Mechanical Engineering 1500 Illinois Street GoldenCO80401 United States

An accurate forecast of electric demand is essential for the optimal design of a generation system. For district installations, the projected lifespan may extend one or two decades. The reliance on a single-year forecast, combined with a fixed load growth rate, is the current industry standard, but does not support a multidecade investment. Existing work on long-term forecasting focuses on annual growth rate and/or uses time resolution that is coarser than hourly. To address the gap, we propose multiple statistical forecast models, verified over as long as an 11-year horizon. Combining demand data, weather data, and occupancy trends results in a hybrid statistical model, i.e., generalized additive model (GAM) with a seasonal autoregressive integrated moving average (SARIMA) of the GAM residuals, a multiple linear regression (MLR) model, and a GAM with ARIMA errors model. We evaluate accuracy based on: (i) annual growth rates of monthly peak loads;(ii) annual growth rates of overall energy consumption;(iii) preservation of daily, weekly, and month-to-month trends that occur within each year, known as the "seasonality" of the data;and, (iv) realistic representation of demand for a full range of weather and occupancy conditions. For example, the models yield an 11-year forecast from a one-year training data set with a normalized root mean square error of 9.091%, a six-year forecast from a one-year training data set with a normalized root mean square error of 8.949%, and a one-year forecast from a 1.2-year training data set with a normalized root mean square error of 6.765%. © 2025, CC BY.

关键词： Electric load forecasting

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Electro-Osmotic Peristaltic Streaming of a Fractional Second-Grade Viscoelastic Nanofluid with Single and Multi-Walled Carbon Nanotubes in a Ciliated Tube

SSRN

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SSRN 2025年

作者： Channakote, Mahadev M. Marudappa, Shekar Bég, O. Anwar Narayana, Mahesha Siddabasappa, C. Department of Mathematics and Statistics M. S. Ramaiah University of Applied Science Karnataka Bengaluru560054 India Department of Mathematics B. M. S. College of Engineering Bengaluru India Multi-Physical Engineering Sciences Group Mechanical Engineering Department Corrosion/Coating Lab. University of Salford 3-08 SEE Building ManchesterM54WT United Kingdom Department of Mathematics The University of the West Indies Mona Campus Kingston Jamaica Bengaluru India

mathematical modelling of carbon nanotubes (CNTs) in biological fluids is crucial for advancing medical applications. Electro-osmotic-driven peristaltic transport, influenced by ciliary motion, plays a significant role in understanding biological flows, including drug delivery, targeted therapy, and biosensing. This study integrates single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with electro-osmotic, heat, and thermal radiation effects in cilia-driven flow. A nanofluid composed of carbon nanotubes suspended in a base fluid is considered. The problem is simplified using the assumptions of long wavelength and low Reynolds number. Caputo's fractional model and Debye-Hückel linearization are employed to analyse the effects of electro-osmosis, natural convection, and heat generation, with lubrication theory providing further simplification. Analytical solutions are derived for key parameters, including electrical potential, axial velocity, temperature, flow rate, and pressure. Axial velocity in the duct's core decreases with a negative Helmholtz-Smoluchowski parameter UUℎs)but increases in the peripheral zones. The reverse occurs with a positive Uℎs. Longer cilia Uβ) and higher electro-osmotic parameter Um) slow core flow and speed up peripheral flow. Higher thermal source UB), thermal Grashof number UGr), and nanotube volume fraction U) boost central axial velocity. Multi-walled CNTs (MWCNTs) yield slightly higher axial velocities than single-walled CNTs (SWCNTs). Temperature rises with UB) but drops with , with MWCNTs reaching higher temperatures. The findings underscore the potential of electro-osmotic peristalsis to enhance fluid transport in confined geometries, offering promising applications in bio-inspired nanofluid propulsion systems and medical micro-pumping technologies. © 2025, The Authors. All rights reserved.

关键词： Reynolds number

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Visualization of Trochlear Dysplasia Using 3-Dimensional Curvature Analysis in Patients With Patellar Instability Facilitates Understanding and Improves the Reliability of the Entry Point to Trochlea Groove Angle

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Arthroscopy, Sports Medicine, and Rehabilitation 2025年第1期7卷 101010-101010页

作者： Sieberer, Johannes M. Park, Nancy Manafzadeh, Armita R. Desroches, Shelby T. Brennan, Kelsey McDonald, Curtis Tommasini, Steven M. Wiznia, Daniel H. Fulkerson, John P. Department of Orthopaedics and Rehabilitation Yale School of Medicine New Haven CT United States Yale Institute for Biospheric Studies Yale University New Haven CT United States Department of Statistics and Data Science Yale University New Haven CT United States Department of Mechanical Engineering and Material Science Yale School of Engineering and Applied Science New Haven CT United States

Purpose: To examine a method to visualize a 3-dimensional (3D) rendered distal femur using 3D curvature analysis and to compare models of patellofemoral instability (PFI) with controls to study the reliability of the entry point to trochlear groove angle (EPTG) metric. Methods: The 3D models of patients with recurrent patellar instability, defined by at least 2 reported patellar dislocation events, and age- and sex-matched controls were created from computed tomography scans. Curvature was calculated to highlight the proximal trochlear ridges and the trochlear groove by overlaying them on the 3D models. Anteroposterior views with and without curvature visualization were created and used for qualitative comparison and to measure the EPTG. The EPTG was measured by 2 raters with and without the aid of the curvature maps. Significant differences between patients with PFI and controls were compared with a Mann-Whitney U test. Inter-rater reliability was calculated using interclass correlation coefficients, classified according to literature and compared using a permutation test. Significance was assumed at .05. Results: Qualitive analysis between 30 PFI patient knees (age: 23.9 ± 8.4 years, female/male: 24/6) and 30 control knees (age: 21.8 ± 5.6 years, female/male: 22/8) showed that in general, patients with PFI have a lateralized medial ridge and trochlear groove, with the trochlear groove being shorter and shallower. Qualitatively, differences between patients with PFI and controls were significant for measurements both with and without the aid of the curvature maps. Inter-rater reliability was significantly (P = .0349) better when using the curvature visualization. Conclusions: Curvature-based visualization aids overlain on a 3D model have the power to increase the information gained from 3D imaging and corresponding 3D models, amplifying their potential value in clinical decision-making. Such visualizations facilitate both the identification of qualitative differenc

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536 Topology optimization for personalized intracranial aneurysm implant design

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Journal of Clinical and Translational Science 2025年第s1期9卷 157-157页

作者： Weijun Lei Chander Sadasivan Shikui Chen Xianfeng David Gu State University of New York at Stony Brook Department of Neurological Surgery Department of Mechanical Engineering Department of Computer Science Department of Applied Mathematics and Statistics

Objectives/Goals: To develop a personalized computational framework integrating computational fluid dynamics (CFD) and topology optimization for designing intracranial aneurysm implants. The primary objective is to reduce intra-aneurysmal blood flow velocity and enhance thrombus formation for improved treatment outcomes. Methods/Study Population: Patient-specific aneurysm geometries were extracted from pre-treatment rotational angiograms. A CFD-driven topology optimization framework was employed to design implants that reduce intra-aneurysmal flow velocity. The fluid dynamics were modeled using Navier–Stokes equations and the structural integrity of the implants was ensured by linear elasticity equations. The solid isotropic material with penalization (SIMP) method was applied to optimize the implant’s porous architecture, balancing flow reduction with structural support. COMSOL Multiphysics software was used to implement the optimization. Results/Anticipated Results: The optimized implants demonstrated significant reductions in intra-aneurysmal blood flow velocity and improved hemodynamic conditions. Flow velocity within the aneurysm was reduced by 77%, and the fluid energy dissipation ratio showed a 78.9% improvement compared to pretreatment conditions. The optimized porous structures were tailored to the aneurysm’s specific geometry, providing personalized designs that improve flow stasis and thrombus formation. Further validation of the implants will be performed in vitro and in vivo to assess their effectiveness and biocompatibility. Discussion/Significance of Impact: This personalized implant design framework could lead to better treatment outcomes by reducing aneurysm recurrence and complications compared to current devices. It provides a pathway for improved occlusion rates and patient-specific solutions for intracranial aneurysms.

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