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On a Dynamic Variant of the Iteratively Regularized Gauss-Newton Method with Sequential Data

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arXiv 2022年

作者： Chada, Neil K. Iglesias, Marco A. Lu, Shuai Werner, Frank Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia School of Mathematical Sciences University of Nottingham NottinghamNG72RD United Kingdom School of Mathematical Sciences Fudan University Shanghai200433 China Institut für Mathematik University of Wuerzburg Emil–Fischer–Str. 30 Würzburg97074 Germany

For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed inverse problems can only be used with a single instance of the observed data, in this work we propose a new framework that enables existing algorithms to invert multiple instances of data in a sequential fashion. Specifically we will work with the well-known iteratively regularized Gauss–Newton method (IRGNM), a variational methodology for solving nonlinear inverse problems. We develop a theory of convergence analysis for a proposed dynamic IRGNM algorithm in the presence of Gaussian white noise. We combine this algorithm with the classical IRGNM to deliver a practical (hybrid) algorithm that can invert data sequentially while producing fast estimates. Our work includes the proof of well-definedness of the proposed iterative scheme, as well as various error bounds that rely on standard assumptions for nonlinear inverse problems. We use several numerical experiments to verify our theoretical findings, and to highlight the benefits of incorporating sequential data. The context of the numerical experiments comprises various parameter identification problems including a Darcy flow PDE, and that of electrical impedance tomography. © 2022, CC BY-NC-SA.

关键词： Inverse problems

Mutually beneficial confluence of structure-based modeling of protein dynamics and machine learning methods

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Current Opinion in Structural Biology 2023年 78卷 102517页

作者： Banerjee, Anupam Saha, Satyaki Tvedt, Nathan C. Yang, Lee-Wei Bahar, Ivet Computational and Systems Biology University of Pittsburgh School of Medicine Pittsburgh 15261 PA United States Computational and Applied Mathematics and Statistics The College of William and Mary Williamsburg 23185 VA United States Institute of Bioinformatics and Structural Biology and PhD Program in Biomedical Artificial Intelligence National Tsing Hua University Hsinchu 300044 Taiwan Physics Division National Center for Theoretical Sciences Taipei 106319 Taiwan

Proteins sample an ensemble of conformers under physiological conditions, having access to a spectrum of modes of motions, also called intrinsic dynamics. These motions ensure the adaptation to various interactions in the cell, and largely assist in, if not determine, viable mechanisms of biological function. In recent years, machine learning frameworks have proven uniquely useful in structural biology, and recent studies further provide evidence to the utility and/or necessity of considering intrinsic dynamics for increasing their predictive ability. Efficient quantification of dynamics-based attributes by recently developed physics-based theories and models such as elastic network models provides a unique opportunity to generate data on dynamics for training ML models towards inferring mechanisms of protein function, assessing pathogenicity, or estimating binding affinities. © 2022 The Authors

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Composite B-Spline Regularized Delta Functions for the Immersed Boundary Method: Divergence-Free Interpolation and Gradient-Preserving Force Spreading

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arXiv 2024年

作者： Gruninger, Cole Griffith, Boyce E. Department of Mathematics University North Carolina Chapel HillNC United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

This paper presents an approach to enhance volume conservation in the immersed boundary (IB) method by employing regularized delta functions derived from composite B-splines. These delta functions are constructed using tensor product kernels, similar to the conventional IB method. However, the kernels are B-splines whose polynomial degree varies according to the normal and tangential directions of each velocity component. The conventional IB method, while effective for fluid-structure interaction applications, has long been challenged by poor volume conservation, particularly evident in simulations of pressurized, closed membranes. We demonstrate that composite B-spline regularized delta functions significantly enhance volume conservation through two complementary properties: they provide continuously divergence-free velocity interpolants and maintain the gradient character of forces corresponding to mean pressure jumps across interfaces. By correctly representing these forces as discrete gradients, they eliminate a key source of spurious flows that typically plague immersed boundary computations. Our approach maintains the local nature of the classical IB method, avoiding the computational overhead associated with the non-local Divergence-Free Immersed Boundary (DFIB) method’s construction of an explicit velocity potential which requires additional Poisson solves for interpolation and force spreading operations. Through a series of numerical experiments, we show that sufficiently regular composite B-spline kernels can maintain initial volumes to within machine precision. We provide a detailed analysis of the relationship between kernel regularity and the accuracy of force spreading and velocity interpolation operations. Our findings indicate that composite B-splines of at least C1 regularity produce results comparable to the DFIB method in dynamic simulations, with errors in volume conservation primarily dominated by truncation error of the employed time-stepping s

关键词： Delta functions

Local Divergence-Free Immersed Finite Element-Difference Method Using Composite B-Splines

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arXiv 2024年

作者： Li, Lianxia Gruninger, Cole Lee, Jae H. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. To address this issue, in simulations involving large deformations of incompressible hyperelastic structures immersed in fluid, researchers often use a volumetric stabilization approach such as adding a volumetric energy term and using modified invariants in the constitutive model of the immersed structure. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook’s membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, CBS kernels achieve convergence on coarser fluid grids, while IB and BS kernels need finer grids for comparable accuracy. Unlike IB and BS ke

关键词： Delta functions

Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order-disorder transitions in LixCoO2

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arXiv 2023年

作者： Teichert, G.H. Das, S. Shojaei, M. Faghih Holber, J. Mueller, T. Hung, L. Gavini, V. Garikipati, K. Department of Mechanical Engineering University of Michigan United States Toyota Research Institute Los AltosCA United States Department of Materials Science & Engineering University of Michigan United States Department of Mathematics University of Michigan United States Michigan Institute for Computational Discovery & Engineering University of Michigan United States Applied Physics Program University of Michigan United States Materials Science & Engineering Johns Hopkins University United States

LixTMO2 (TM=Ni, Co, Mn) forms an important family of cathode materials for Li-ion batteries, whose performance is strongly governed by Li composition-dependent crystal structure and phase stability. Here, we use LixCoO2 (LCO) as a model system to benchmark a machine learning-enabled framework for bridging scales in materials physics. We focus on two scales: (a) assemblies of thousands of atoms described by density functional theory-informed statistical mechanics, and (b) continuum phase field models to study the dynamics of order-disorder transitions in LCO. Central to the scale bridging is the rigorous, quantitatively accurate, representation of the free energy density and chemical potentials of this material system by coarsegraining formation energies for specific atomic configurations. We develop active learning workflows to train recently developed integrable deep neural networks for such high-dimensional free energy density and chemical potential functions. The resulting, first principles-informed, machine learning-enabled, phase-field computations allow us to study LCO cathodes’ phase evolution in terms of temperature, morphology, charge cycling and particle size. © 2023, CC BY-NC-SA.

关键词： Cathodes

Flagellum Pumping Efficiency in Shear-Thinning Viscoelastic Fluids

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arXiv 2023年

作者： Barrett, Aaron Fogelson, Aaron L. Gregory Forest, M. Gruninger, Cole Lim, Sookkyung Griffith, Boyce E. Department of Mathematics University of Utah Salt Lake CityUT United States Departments of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Department of Mathematical Sciences University of Cincinnati CincinnatiOH United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear-thinning of the viscoelastic environment. Copyright © 2023, The Authors. All rights reserved.

关键词： Shear thinning

An optimal algorithm for strict circular seriation

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arXiv 2021年

作者： Armstrong, Santiago Guzmán, Cristóbal Long, Carlos A. Sing Institute for Mathematical and Computational Engineering Pontificia Universidad Católica de Chile Santiago Chile Anid - Millennium Science Initiative Program Millennium Nucleus Center for the Discovery of Structures in Complex Data Santiago Chile Department of Applied Mathematics University of Twente Netherlands Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Santiago Chile

We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between n objects, and the goal is to find a circular order of the objects in a manner that is consistent with their dissimilarity. This problem is a generalization of the classical linear seriation problem where the goal is to find a linear order, and for which optimal O(n2) algorithms are known. Our contributions can be summarized as follows. First, we introduce circular Robinson matrices as the natural class of dissimilarity matrices for the circular seriation problem. Second, for the case of strict circular Robinson dissimilarity matrices we provide an optimal O(n2) algorithm for the circular seriation problem. Finally, we propose a statistical model to analyze the well-posedness of the circular seriation problem for large n. In particular, we establish O(log(n)/n) rates on the distance between any circular ordering found by solving the circular seriation problem to the underlying order of the model, in the Kendall-tau *** Codes 68R01, 05C85, 05C50, 05C25, 65C20 Copyright © 2021, The Authors. All rights reserved.

关键词： Trees (mathematics)

Correction to: Optimal deterministic algorithm generation

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Journal of Global Optimization 2018年第2期73卷 465-465页

作者： Mitsos, Alexander Najman, Jaromił Kevrekidis, Ioannis G. AVT Process Systems Engineering (SVT) RWTH Aachen University Aachen Germany Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics Princeton University Princeton USA IAS-TUM Garching and Zuse Institut FU Berlin Berlin Germany Departments of Chemical and Biomolecular Engineering Applied Mathematics and Statistics and Urology Johns Hopkins University Baltimore USA

Unfortunately, the copyright information of the article in Springerlink appears as “©  Springer Science+Business Media, LLC, part of Springer Nature 2018” this has been corrected to “©  ...

Unfortunately, the copyright information of the article in Springerlink appears as “© Springer Science+Business Media, LLC, part of Springer Nature 2018” this has been corrected to “© The Author(s) 2018.”

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The putative center in NGC 1052

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arXiv 2025年

作者： Baczko, Anne-Kathrin Kadler, Matthias Ros, Eduardo Fromm, Christian M. Wielgus, Maciek Perucho, Manel Krichbaum, Thomas P. Baloković, Mislav Blackburn, Lindy Chan, Chi-Kwan Issaoun, Sara Janssen, Michael Ricci, Luca Akiyama, Kazunori Albentosa-Ruíz, Ezequiel Alberdi, Antxon Alef, Walter Algaba, Juan Carlos Anantua, Richard Asada, Keiichi Azulay, Rebecca Bach, Uwe Ball, David Bandyopadhyay, Bidisha Barrett, John Bauböck, Michi Benson, Bradford A. Bintley, Dan Blundell, Raymond Bouman, Katherine L. Bower, Geoffrey C. Boyce, Hope Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bronzwaer, Thomas Bustamante, Sandra Byun, Do-Young Carlstrom, John E. Ceccobello, Chiara Chael, Andrew Chang, Dominic O. Chatterjee, Koushik Chatterjee, Shami Chen, Ming-Tang Chen, Yongjun Cheng, Xiaopeng Cho, Ilje Christian, Pierre Conroy, Nicholas S. Conway, John E. Cordes, James M. Crawford, Thomas M. Crew, Geoffrey B. Cruz-Osorio, Alejandro Cui, Yuzhu Dahale, Rohan Davelaar, Jordy De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dexter, Jason Dhruv, Vedant Dihingia, Indu K. Doeleman, Sheperd S. Dougall, Sean Taylor Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fish, Vincent L. Fomalont, Edward Ford, H. Alyson Foschi, Marianna Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fuentes, Antonio Galison, Peter Gammie, Charles F. García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gold, Roman Gómez-Ruiz, Arturo I. Gómez, José L. Gu, Minfeng Gurwell, Mark Hada, Kazuhiro Haggard, Daryl Haworth, Kari Hecht, Michael H. Hesper, Ronald Heumann, Dirk Ho, Luis C. Ho, Paul Honma, Mareki Huang, Chih-Wei L. Huang, Lei Hughes, David H. Impellizzeri, C.M. Violette Inoue, Makoto James, David J. Jannuzi, Buell T. Jeter, Britton Jiang, Wu Jiménez-Rosales, Alejandra Johnson, Michael D. Jorstad, Svetlana Joshi, Abhishek V. Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, M Department of Space Earth and Environment Chalmers University of Technology GothenburgSE-41296 Sweden Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Institut für Theoretische Physik und Astrophysik Universität Würzburg Emil-Fischer-Str. 31 WürzburgD-97074 Germany Institut für Theoretische Physik Goethe-Universität Frankfurt Max-von-Laue-Straße 1 Frankfurt am MainD-60438 Germany Departament d'Astronomia i Astrofísica Universitat de València C. Dr. Moliner 50 Burjassot ValènciaE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 Paterna ValènciaE-46980 Spain Yale Center for Astronomy & Astrophysics Yale University 52 Hillhouse Avenue New HavenCT06511 United States Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Ave. TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 N. Santa Rita TucsonAZ85721 United States Radboud University PO Box 9010 Nijmegen6500 GL Netherlands Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Department of Physics Faculty of Science Universiti Malaya Kuala Lumpur50603 Malaysia Department of Physics & Astronomy The University of Texas at San Antonio One UTSA Circle San AntonioTX78249 United States Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd. Taipei10617 Taiwan Astronomy Depart

Context. Many active galaxies harbor powerful relativistic jets, however, the detailed mechanisms of their formation and acceleration remain poorly understood. Aims. To investigate the area of jet acceleration and collimation with the highest available angular resolution, we study the innermost region of the bipolar jet in the nearby low-ionization nuclear emission-line region (LINER) galaxy NGC 1052. Methods. We combined observations of NGC 1052 taken with VLBA, GMVA, and EHT over one week in the spring of 2017. Our study is focused on the size and continuum spectrum of the innermost region containing the central engine and the footpoints of both jets. We employed a synchrotron-self absorption model to fit the continuum radio spectrum and we combined the size measurements from close to the central engine out to ∼1 pc to study the jet collimation. Results. For the first time, NGC 1052 was detected with the EHT, providing a size of the central region in-between both jet bases of 43 µas perpendicular to the jet axes, corresponding to just around 250 RS (Schwarzschild radii). This size estimate supports previous studies of the jets expansion profile which suggest two breaks of the profile at around 3 × 103 RS and 1 × 104 RS distances to the core. Furthermore, we estimated the magnetic field to be 1.25 Gauss at a distance of 22 µas from the central engine by fitting a synchrotron-self absorption spectrum to the innermost emission feature, which shows a spectral turn-over at ∼130 GHz. Assuming a purely poloidal magnetic field, this implies an upper limit on the magnetic field strength at the event horizon of 2.6 × 104 Gauss, which is consistent with previous measurements. Conclusions. The complex, low-brightness, double-sided jet structure in NGC 1052 makes it a challenge to detect the source at millimeter (mm) wavelengths. However, our first EHT observations have demonstrated that detection is possible up to at least 230 GHz. This study offers a glimpse through the dens

关键词： Synchrotrons