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Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations

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arXiv 2023年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas 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 Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location

Preconditioning hyperbolic 5-equation two-phase model in intermittent pipe flow simulations

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AIP Conference Proceedings 2024年第1期3094卷

作者： Farhad Nikfarjam Hamid Reza Anbarlooei Daniel O. A. Cruz Department of Applied Mathematics Institute of Mathematics Federal University of Rio de Janeiro RJ Brazil Mechanical Engineering Program Institute of Mathematics Federal University of Rio de Janeiro RJ Brazil

The 5-equation unconditionally hyperbolic formulation of the two-fluid model solved by Roe’s method is studied. It is well-known that the 5-equation upwind methods experience loss of accuracy at low Mach numbers. To address this issue, a preconditioning technique is developed to control the numerical dissipation at low velocities. The resulting method is evaluated on different test cases, and is observed that the preconditioned first order Roe method limits the numerical dissipation, comparable to the second order method without preconditioning. The method is used to study 1D intermittent two-phase flow in pipelines. Our method successfully captures the slugs and predicts the statistics of the flow accurately, for the cases where other methods could not capture a slug flow at all or have serious shortcomings.

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Neutrinos and Gamma Rays from Beta Decays in an Active Galactic Nucleus NGC 1068 Jet

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Physical Review Letters 2025年第15期134卷 151005-151005页

作者： Koichiro Yasuda Nobuyuki Sakai Yoshiyuki Inoue Alexander Kusenko Department of Physics and Astronomy University of California Los Angeles Los Angeles California 90095-1547 USA Department of Earth and Space Science Graduate School of Science Osaka University Toyonaka Osaka 560-0043 Japan Interdisciplinary Theoretical & Mathematical Science Program (iTHEMS) RIKEN 2-1 Hirosawa Saitama 351-0198 Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI) UTIAS The University of Tokyo Kashiwa Chiba 277-8583 Japan

We show that TeV neutrinos and high-energy gamma rays detected from the nearby active galaxy NGC 1068 can simultaneously be explained in a model based on the beta decays of neutrons produced in the photodisintegration of He4 nuclei on ultraviolet photons in the jet. The photodisintegration of nuclei occurs at energies above several PeV, which explains the 1–100 TeV energies of the observed neutrinos. The TeV gamma-ray flux accompanying the beta decays is expected to be much lower than the neutrino flux, which agrees with the observations of NGC 1068 showing a gamma-ray deficit as compared to the expectations from proton-photon interactions. Furthermore, the synchrotron and inverse Compton gamma-ray flux associated with protons’ Bethe-Heitler pair production and the photopion processes in the jet can be consistent with the observed gamma-ray flux at GeV energies for a plausible range of magnetic fields of jets. This scenario, combining beta decay and Bethe-Heitler, can be applied to other jet Seyfert galaxies such as NGC 4151. Future measurements of the neutrino flavor ratio can help confirm the beta-decay origin of the observed neutrinos.

关键词： Active Galactic Nuclei

Classical and Quantum Phase Transitions in Multiscale Media: Universality and Critical Exponents in the Fractional Ising Model

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arXiv 2025年

作者： Lewis, Joshua M. Carr, Lincoln D. Quantum Engineering Program Colorado School of Mines 1523 Illinois St. GoldenCO80401 United States Department of Physics Colorado School of Mines 1523 Illinois St. GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1523 Illinois St. GoldenCO80401 United States

Until now multiscale quantum problems have appeared to be out of reach at the many-body level relevant to strongly correlated materials and current quantum information devices. In fact, they can be modeled with q-th order fractional derivatives, as we demonstrate in this work, treating classical and quantum phase transitions in a fractional Ising model for 0 D of the system tied geometrically to the anomalous dimension η. We discover that for classical systems, HD is precisely equal to the fractional order q. In contrast, for quantum systems, HD deviates from this direct equivalence, scaling more gradually, driven by additional degrees of freedom introduced by quantum fluctuations. These results reveal how fractional derivatives fundamentally modify the fractal geometry of many-body interactions, directly influencing the universal symmetries of the system and overcoming traditional dimensional restrictions on phase transitions. Specifically, we find that for q © 2025, CC BY.

关键词： Degrees of freedom (mechanics)

Learning shared neural manifolds from multi-subject FMRI data

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arXiv 2021年

作者： Huang, Jessie Busch, Erica L. Wallenstein, Tom Gerasimiuk, Michal Benz, Andrew Lajoie, Guillaume Wolf, Guy Turk-Browne, Nicholas B. Krishnaswamy, Smita Department Of Computer Science Department Of Psychology Department Of Mathematics Department Of Genetics Program In Applied Mathematics Wu Tsai Institute Yale University United States Department Of Mathematics And Statistics Université De Montréal Canada Mila Quebec AI Institute Canada

Functional magnetic resonance imaging (fMRI) is a notoriously noisy measurement of brain activity because of the large variations between individuals, signals marred by environmental differences during collection, and spatiotemporal averaging required by the measurement resolution. In addition, the data is extremely high dimensional, with the space of the activity typically having much lower intrinsic dimension. In order to understand the connection between stimuli of interest and brain activity, and analyze differences and commonalities between subjects, it becomes important to learn a meaningful embedding of the data that denoises, and reveals its intrinsic structure. Specifically, we assume that while noise varies significantly between individuals, true responses to stimuli will share common, low-dimensional features between subjects which are jointly discoverable. Similar approaches have been exploited previously but they have mainly used linear methods such as PCA and shared response modeling (SRM). In contrast, we propose a neural network called MRMD-AE (manifold-regularized multiple decoder, autoencoder), that learns a common embedding from multiple subjects in an experiment while retaining the ability to decode to individual raw fMRI signals. We show that our learned common space represents an extensible manifold (where new points not seen during training can be mapped), improves the classification accuracy of stimulus features of unseen timepoints, as well as improves cross-subject translation of fMRI signals. We believe this framework can be used for many downstream applications such as guided brain-computer interface (BCI) training in the future. Copyright © 2021, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

Correction to: Generalized Semi-infinite Polynomial Optimization and Semidefinite programming Relaxations

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Acta Mathematica Vietnamica 2024年 1-1页

作者： Jiao, Liguo Lee, Jae Hyoung Phạm, Tiến-Sơn Academy for Advanced Interdisciplinary Studies Northeast Normal University Changchun China Shanghai Zhangjiang Institute of Mathematics Shanghai China Department of Applied Mathematics Pukyong National University Busan Republic of Korea Department of Mathematics Dalat University Dalat Vietnam

Scaling limits of external multi-particle DLA on the plane and the supercooled stefan problem

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arXiv 2021年

作者： Nadtochiy, Sergey Shkolnikov, Mykhaylo Zhang, Xiling Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States ORFE Department Bendheim Center for Finance Program in Applied & Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider (a variant of) the external multi-particle diffusion-limited aggregation (MDLA) process of Rosenstock and Marquardt on the plane. Based on the recent findings of [11], [10] in one space dimension it is natural to conjecture that the scaling limit of the growing aggregate in such a model is given by the growing solid phase in a suitable "probabilistic" formulation of the single-phase supercooled Stefan problem for the heat equation. To address this conjecture, we extend the probabilistic formulation from [10] to multiple space dimensions. We then show that the equation that characterizes the growth rate of the solid phase in the supercooled Stefan problem is satisfied by the scaling limit of the external MDLA process with an inequality, which can be strict in general. In the course of the proof, we establish two additional results interesting in their own right: (i) the stability of a "crossing property" of planar Brownian motion and (ii) a rigorous connection between the probabilistic solutions to the supercooled Stefan problem and its classical and weak *** Codes 82C22, 80A22, 60H30 Copyright © 2021, The Authors. All rights reserved.

关键词： Supercooling

PHYSICS INFORMED MACHINE LEARNING WITH SMOOTHED PARTICLE HYDRODYNAMICS: HIERARCHY OF REDUCED LAGRANGIAN MODELS OF TURBULENCE

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arXiv 2021年

作者： Woodward, Michael Tian, Yifeng Hyett, Criston Fryer, Chris Stepanov, Mikhail Livescu, Daniel Chertkov, Michael Graduate Interdisciplinary Program in Applied Mathematics UArizona TucsonAZ85721 United States Department of Mathematics UArizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division LANL Los AlamosNM87544 United States

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH;and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales. Copyright © 2021, The Authors. All rights reserved.

关键词： Parameterization

Efficient subgroup testing in change-plane models

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arXiv 2024年

作者： Liu, Xu Huang, Jian Zhou, Yong Zhang, Feipeng Ren, Panpan School of Statistics and Management Shanghai University of Finance and Economics Shanghai200433 China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong Academy of Statistics and Interdisciplinary Sciences East China Normal University Shanghai200062 China School of Economics and Finance Xi’an Jiaotong University Xi’an710049 China

Considered here is a hypothesis test for the coefficients in the change-plane regression models to detect the existence of a change plane. The test that is considered is from the class of test problems in which some parameters are not identifiable under the null hypothesis. The classic exponential average tests do not work well in practice. To overcome this drawback, a novel test statistic is proposed by taking the weighted average of the squared score test statistic (WAST) over the grouping parameter’s space, which has a closed form from the perspective of the conjugate priors when an appropriate weight is chosen. The WAST significantly improves the power in practice, particularly in cases where the number of the grouping variables is large. The asymptotic distributions of the WAST are derived under the null and alternative hypotheses. The approximation of critical value by the bootstrap method is investigated, which is theoretically guaranteed. Furthermore, the proposed test method is naturally extended to the generalized estimating equation (GEE) framework, as well as multiple change planes that can test if there are three or more subgroups. The WAST performs well in simulation studies, and its performance is further validated by applying it to real datasets. Copyright © 2024, The Authors. All rights reserved.

关键词： Logistic regression