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Journal articles on the topic 'Infinite-width limit'

Author: Grafiati

Published: 7 July 2024

Last updated: 31 July 2025

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1

Bahri, Yasaman, Boris Hanin, Antonin Brossollet, et al. "Les Houches lectures on deep learning at large and infinite width^*." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 10 (2024): 104012. http://dx.doi.org/10.1088/1742-5468/ad2dd3.

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Abstract These lectures, presented at the 2022 Les Houches Summer School on Statistical Physics and Machine Learning, focus on the infinite-width limit and large-width regime of deep neural networks. Topics covered include the various statistical and dynamical properties of these networks. In particular, the lecturers discuss properties of random deep neural networks, connections between trained deep neural networks, linear models, kernels and Gaussian processes that arise in the infinite-width limit, and perturbative and non-perturbative treatments of large but finite-width networks, at initi

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2

Pastur, L. "Eigenvalue distribution of large random matrices arising in deep neural networks: Orthogonal case." Journal of Mathematical Physics 63, no. 6 (2022): 063505. http://dx.doi.org/10.1063/5.0085204.

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This paper deals with the distribution of singular values of the input–output Jacobian of deep untrained neural networks in the limit of their infinite width. The Jacobian is the product of random matrices where the independent weight matrices alternate with diagonal matrices whose entries depend on the corresponding column of the nearest neighbor weight matrix. The problem has been considered in the several recent studies of the field for the Gaussian weights and biases and also for the weights that are Haar distributed orthogonal matrices and Gaussian biases. Based on a free probability argu

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3

Pacelli, R., S. Ariosto, M. Pastore, F. Ginelli, M. Gherardi, and P. Rotondo. "A statistical mechanics framework for Bayesian deep neural networks beyond the infinite-width limit." Nature Machine Intelligence 5, no. 12 (2023): 1497–507. http://dx.doi.org/10.1038/s42256-023-00767-6.

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4

Thorkildsen, Gunnar, and Helge B. Larsen. "X-ray diffraction in perfect t × l crystals. Rocking curves." Acta Crystallographica Section A Foundations of Crystallography 55, no. 5 (1999): 840–54. http://dx.doi.org/10.1107/s0108767399002986.

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A general formalism, based on the Takagi–Taupin equations, for calculating rocking curves in perfect t\times l crystals is presented. It includes nonsymmetrical scattering, refraction, and ordinary and anomalous absorption. t and l may be varied independently. In the limit of a semi-infinite crystal, the standard results from the fundamental theory are retrieved. For crystal dimensions less than the extinction length, the theory converges to the kinematical limit. Simulations for germanium and silicon show significant influence of crystal finiteness. When dynamical effects are prominent, the c

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5

Karr, D. G., J. C. Watson, and M. HooFatt. "Three-Dimensional Analysis of Ice Sheet Indentation: Limit Analysis Solutions." Journal of Offshore Mechanics and Arctic Engineering 111, no. 1 (1989): 63–69. http://dx.doi.org/10.1115/1.3257141.

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A method is presented for determining the collapse pressures of an ice sheet subjected to a uniformly distributed edge load by applying the upper-bound theorem of limit analysis. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. A quadratic anisotropic yield criterion is used to calculate the indentation pressures. The ice sheet consists of columnar ice and is assumed isotropic in the plane of the ice sheet. Upper-bound solutions are found by optimizing a three-dimensional discontinuous velocity field representing an assumed collapse pattern of the ice

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6

Landa, Haggai, Cecilia Cormick, and Giovanna Morigi. "Static Kinks in Chains of Interacting Atoms." Condensed Matter 5, no. 2 (2020): 35. http://dx.doi.org/10.3390/condmat5020035.

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We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n ≥ 1 . The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but

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7

AKHMEDIEV, N., J. M. SOTO-CRESPO, M. GRAPINET, and Ph GRELU. "DISSIPATIVE SOLITON PULSATIONS WITH PERIODS BEYOND THE LASER CAVITY ROUND TRIP TIME." Journal of Nonlinear Optical Physics & Materials 14, no. 02 (2005): 177–94. http://dx.doi.org/10.1142/s0218863505002645.

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We review recent results on periodic pulsations of the soliton parameters in a passively mode-locked fiber laser. Solitons change their shape, amplitude, width and velocity periodically in time. These pulsations are limit cycles of a dissipative nonlinear system in an infinite-dimensional phase space. Pulsation periods can vary from a few to hundreds of round trips. We present a continuous model of a laser as well as a model with parameter management. The results of the modeling are supported with experimental results obtained using a fiber laser.

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8

Bordelon, Blake, and Cengiz Pehlevan. "Dynamics of finite width Kernel and prediction fluctuations in mean field neural networks^*." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 10 (2024): 104021. http://dx.doi.org/10.1088/1742-5468/ad642b.

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Abstract We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the O ( 1 / width ) fluctuations of the dynamical mean field theory order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. We find that once the mean field/µP parameterization is adopted, the le

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9

Wang, Xu, Faning Dang, Xiaoshan Cao, Le Zhang, Jun Gao, and Haibin Xue. "Solution for Active and Passive Earth Pressure on Rigid Retaining Walls with Narrow Backfill." Applied Sciences 15, no. 4 (2025): 1750. https://doi.org/10.3390/app15041750.

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For a retaining wall adjacent to rock or rigid structures, existing model test results indicate that the slip soil in the limit state can be approximated as a trapezoidal slip wedge. Based on the static equilibrium condition of the slip wedge, a calculation method for active and passive earth pressures is proposed that considers the effect of backfill width through extreme value analysis. As the backfill width increases, the trapezoidal slip wedge transitions to a triangular slip wedge, introducing a critical width to distinguish between finite and semi-infinite soil conditions. For cohesionle

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10

Zeng, Y., and S. Weinbaum. "Stokes flow through periodic orifices in a channel." Journal of Fluid Mechanics 263 (March 25, 1994): 207–26. http://dx.doi.org/10.1017/s0022112094004088.

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This paper develops a three-dimensional infinite series solution for the Stokes flow through a parallel walled channel which is obstructed by a thin planar barrier with periodically spaced rectangular orifices of arbitrary aspect ratio B’/d’ and spacing D’. Here B’ is the half-height of the channel and d’ is the half-width of the orifice. The problem is motivated by recent electron microscopic studies of the intercellular channel between vascular endothelial cells which show a thin junction strand barrier with discontinuities or breaks whose spacing and width vary with the tissue. The solution

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11

DELEBECQUE, FANNY. "AN ASYMPTOTIC MODEL FOR THE TRANSPORT OF AN ELECTRON GAS IN A SLAB." Mathematical Models and Methods in Applied Sciences 21, no. 07 (2011): 1443–78. http://dx.doi.org/10.1142/s0218202511005453.

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We study the limiting behavior of a Schrödinger–Poisson system describing a three-dimensional quantum gas that is confined along the vertical z-direction in a fine slab. The starting point is the three-dimensional Schrödinger–Poisson system with Dirichlet conditions on two horizontal planes z = 0 and z = ε, where the small parameter ε is the scale width of the slab. The limit ε → 0 appears to be an infinite system of two-dimensional nonlinear Schrödinger equations. Our strategy combines a refined analysis of the Poisson kernel acting on strongly confined densities and a time-averaging process

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VOJTA, MATTHIAS, YING ZHANG, and SUBIR SACHDEV. "RENORMALIZATION GROUP ANALYSIS OF QUANTUM CRITICAL POINTS IN d-WAVE SUPERCONDUCTORS." International Journal of Modern Physics B 14, no. 29n31 (2000): 3719–34. http://dx.doi.org/10.1142/s0217979200004271.

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We describe a search for renormalization group fixed points which control a second-order quantum phase transition between a dx2-y2-superconductor and some other superconducting ground state. Only a few candidate fixed points are found. In the finite temperature (T) quantum-critical region of some of these fixed points, the fermion quasiparticle lifetime is very short and the spectral function has an energy width of order kBT near the Fermi points. Under the same conditions, the thermal conductivity is infinite in the scaling limit. We thus provide simple, explicit, examples of quantum theories

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13

Jagannathan, Arjun, Kraig Winters, and Laurence Armi. "Stratified Flows over and around Long Dynamically Tall Mountain Ridges." Journal of the Atmospheric Sciences 76, no. 5 (2019): 1265–87. http://dx.doi.org/10.1175/jas-d-18-0145.1.

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Abstract Uniformly stratified flows approaching long and dynamically tall ridges develop two distinct flow components over disparate time scales. The fluid upstream and below a “blocking level” is stagnant in the limit of an infinite ridge and flows around the sides when the ridge extent is finite. The streamwise half-width of the obstacle at the blocking level arises as a natural inner length scale for the flow, while the excursion time over this half-width is an associated short time scale for the streamwise flow evolution. Over a longer time scale, low-level horizontal flow splitting leads

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14

Ghosal, Sandip, and John D. Sherwood. "Screened Coulomb interactions with non-uniform surface charge." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2199 (2017): 20160906. http://dx.doi.org/10.1098/rspa.2016.0906.

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The screened Coulomb interaction between a pair of infinite parallel planes with spatially varying surface charge is considered in the limit of small electrical potentials for arbitrary Debye lengths. A simple expression for the disjoining pressure is derived in terms of a two-dimensional integral in Fourier space. The integral is evaluated for periodic and random charge distributions and the disjoining pressure is expressed as a sum over Fourier–Bloch reciprocal lattice vectors or in terms of an integral involving the autocorrelation function, respectively. The force between planes with a fin

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15

Yang, Mimi X., Fuqian Yang, and Sanboh Lee. "Dielectric breakdown sizes of conducting plates." IMA Journal of Applied Mathematics 86, no. 3 (2021): 502–13. http://dx.doi.org/10.1093/imamat/hxab013.

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Abstract In this work, we propose mathematical formulations that detail the effect of the dielectric strength of dielectric material on the spatial distribution of electric field in an infinite space with a conducting plate. Using the dielectric strength of air as the maximum limit for the magnitude of electric field intensity and the equivalence of stored charge between two different zones, we determine the size of the dielectric breakdown region (the extended region with ionized material) for the conducting strip and the conducting disk charged to an electric voltage. The size of dielectric

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16

MELLO, D. F. DE, and G. G. CABRERA. "LOCAL ORDER AND MAGNETIC FIELD EFFECTS ON THE ELECTRONIC PROPERTIES OF DISORDERED BINARY ALLOYS IN THE QUANTUM SITE PERCOLATION LIMIT." International Journal of Modern Physics B 13, no. 32 (1999): 3861–77. http://dx.doi.org/10.1142/s0217979299004057.

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Electronic properties of disordered binary alloys are studied via the calculation of the average Density of States (DOS) in two and three dimensions. We propose a new approximate scheme that allows for the inclusion of local order effects in finite geometries and extrapolates the behavior of infinite systems following finite-size scaling ideas. We particularly investigate the limit of the Quantum Site Percolation regime described by a tight-binding Hamiltonian. This limit was chosen to probe the role of short range order (SRO) properties under extreme conditions. The method is numerically high

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17

Karr, D. G. "Three-Dimensional Analysis of Ice Sheet Indentation: Lower-Bound Solutions." Journal of Offshore Mechanics and Arctic Engineering 110, no. 1 (1988): 81–86. http://dx.doi.org/10.1115/1.3257128.

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The methods of plastic limit analysis are used to determine the indentation pressures of a flat rigid punch on a columnar ice sheet. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. Representative strength parameters of columnar sea ice are used to define anisotropic yield criteria for the ice sheet. The anisotropic yield criteria reflect the variations in mechanical properties caused by the horizontal orientation of the c-axis of sea ice in the columnar zone. Numerical results are obtained by applying the lower-bound theorem of plastic limit analysis.

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18

Erbin, H., V. Lahoche, and D. Ousmane Samary. "Non-perturbative renormalization for the neural network-QFT correspondence." Machine Learning: Science and Technology 3, no. 1 (2022): 015027. http://dx.doi.org/10.1088/2632-2153/ac4f69.

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Abstract In a recent work (Halverson et al 2021 Mach. Learn.: Sci. Technol. 2 035002), Halverson, Maiti and Stoner proposed a description of neural networks (NNs) in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory while finite N corrections are taken into account by interactions (non-Gaussian terms in the action). In this paper, we study two related aspects of this correspondence. First, we comment on the concepts of locality and power-counting in this context. Indeed, these usual space-time notions may not hold for NNs (since inputs can b

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19

Spetzler, Jesper, and Roel Snieder. "The Fresnel volume and transmitted waves." GEOPHYSICS 69, no. 3 (2004): 653–63. http://dx.doi.org/10.1190/1.1759451.

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In seismic imaging experiments, it is common to use a geometric ray theory that is an asymptotic solution of the wave equation in the high‐frequency limit. Consequently, it is assumed that waves propagate along infinitely narrow lines through space, called rays, that join the source and receiver. In reality, recorded waves have a finite‐frequency content. The band limitation of waves implies that the propagation of waves is extended to a finite volume of space around the geometrical ray path. This volume is called the Fresnel volume. In this tutorial, we introduce the physics of the Fresnel vo

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20

Hewitt, R. E., P. W. Duck, and A. J. Williams. "Injection into boundary layers: solutions beyond the classical form." Journal of Fluid Mechanics 822 (June 7, 2017): 617–39. http://dx.doi.org/10.1017/jfm.2017.288.

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This theoretical and numerical study presents three-dimensional boundary-layer solutions for laminar incompressible flow adjacent to a semi-infinite flat plate, subject to a uniform free-stream speed and injection through the plate surface. The novelty in this case arises from a fully three-dimensional formulation, which also allows for slot injection over a spanwise length scale comparable to the boundary-layer thickness. This approach retains viscous effects in both the spanwise and transverse directions, and effectively results in a parabolised Navier–Stokes system (sometimes referred to as

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21

Babeshko, V. A., O. V. Evdokimova, O. M. Babeshko, V. S. Evdokimov, and M. V. Zaretskaya. "EXACT SOLUTION OF CONTACT PROBLEMS IN A FINITE-WIDTH BAND ON A MULTILAYER MEDIUM." Problems of Strength and Plasticity 85, no. 1 (2023): 36–44. http://dx.doi.org/10.32326/1814-9146-2023-85-1-36-44.

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In this paper, for the first time, an exact solution of contact problems for rigid or deformable stamps in a strip of finite width is obtained. It is assumed that the strip is located on a multilayer base of finite thickness. The universal modeling method previously developed by the authors is used. With its help, the solutions of complex boundary value problems for systems of partial differential equations are reduced, using the Galerkin transform, to solving individual differential equations, among which the Helmholtz equations are the simplest. In an earlier work of the authors published, w

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22

CASTRO, IAN P. "Weakly stratified laminar flow past normal flat plates." Journal of Fluid Mechanics 454 (March 10, 2002): 21–46. http://dx.doi.org/10.1017/s0022112001007248.

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Numerical computations of the steady, two-dimensional, incompressible, uniform velocity but stably stratified flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the stratification is weak enough to avoid occurrence of the gravity wave motions familiar in more strongly stratified flows over obstacles. The nature of the flow is explored for channel half-widths, H, in the range 5 [les ] H [les ] 100, for Reynolds numbers, Re, (based on body half-width and the upstream velocity, U) up to 600 and for stratification levels between

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23

Borcea, L., J. Garnier, and K. Sølna. "Onset of energy equipartition among surface and body waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2246 (2021): 20200775. http://dx.doi.org/10.1098/rspa.2020.0775.

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We derive a radiative transfer equation that accounts for coupling from surface waves to body waves and the other way around. The model is the acoustic wave equation in a two-dimensional waveguide with reflecting boundary. The waveguide has a thin, weakly randomly heterogeneous layer near the top surface, and a thick homogeneous layer beneath it. There are two types of modes that propagate along the axis of the waveguide: those that are almost trapped in the thin layer, and thus model surface waves, and those that penetrate deep in the waveguide, and thus model body waves. The remaining modes

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24

Onofrei, Daniel, and Andrew E. Thaler. "Anomalous Localized Resonance Phenomena in the Nonmagnetic, Finite-Frequency Regime." Advances in Mathematical Physics 2016 (2016): 1–28. http://dx.doi.org/10.1155/2016/4156072.

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The phenomenon of anomalous localized resonance (ALR) is observed at the interface between materials with positive and negative material parameters and is characterized by the fact that when a given source is placed near the interface, the electric and magnetic fields start to have very fast and large oscillations around the interface as the absorption in the materials becomes very small while they remain smooth and regular away from the interface. In this paper, we discuss the phenomenon of anomalous localized resonance (ALR) in the context of an infinite slab of homogeneous, nonmagnetic mate

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25

Ren, He, and Wei-Feng Sun. "Characterizing Dielectric Permittivity of Nanoscale Dielectric Films by Electrostatic Micro-Probe Technology: Finite Element Simulations." Sensors 19, no. 24 (2019): 5405. http://dx.doi.org/10.3390/s19245405.

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Finite element simulations for detecting the dielectric permittivity of planar nanoscale dielectrics by electrostatic probe are performed to explore the microprobe technology of characterizing nanomaterials. The electrostatic force produced by the polarization of nanoscale dielectrics is analyzed by a capacitance gradient between the probe and nano-sample in an electrostatic detection system, in which sample thickness is varied in the range of 1 nm–10 μm, the width (diameter) encompasses from 100 nm to 10 μm, the tilt angle of probe alters between 0° and 20°, and the relative dielectric consta

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26

Kilani, M. I., A. Al-Salaymeh, and A. T. Al-Halhouli. "Effect of Channel Aspect Ratio on the Flow Performance of a Spiral-Channel Viscous Micropump." Journal of Fluids Engineering 128, no. 3 (2005): 618–27. http://dx.doi.org/10.1115/1.2175169.

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The paper investigates the effect of channel aspect ratio on the flow performance of a newly introduced spiral-channel viscous micropump. An approximate 2D analytical solution for the flow field, which ignores channel curvature but accounts for a finite wall height, is first developed at the lubrication limit. A number of 3D models for spiral pumps with different aspect ratios are then built and analyzed using the finite volume method. Numerical and analytical results are in good agreement and tend to support one another. The results are compared with an approximate 2D analytical solution deve

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27

Bokov, S. S., and R. N. Shmatkov. "On asymptotic features of n-spheres." Izvestiya vuzov. Investitsii. Stroitelstvo. Nedvizhimost 15, no. 1 (2025): 64–72. https://doi.org/10.21285/2227-2917-2025-1-64-72.

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As an object of computer simulation, a three-dimensional sphere is used in many areas of contemporary science and technology due to its convenience, simplicity, and versatility. An increased number of parameters for contemporary models complicates the limiting area of simulation parameters to an n-dimensional sphere (n-sphere). For example, a four-dimensional sphere used in astronomy to simulate the movement of celestial bodies includes a fourth parameter of time in addition to the length, width, and height of material point movement. In other areas of science, the growing number of simulation

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Fujioka, Hideki, and James B. Grotberg. "Steady Propagation of a Liquid Plug in a Two-Dimensional Channel." Journal of Biomechanical Engineering 126, no. 5 (2004): 567–77. http://dx.doi.org/10.1115/1.1798051.

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In this study, we investigate the steady propagation of a liquid plug within a two-dimensional channel lined by a uniform, thin liquid film. The Navier-Stokes equations with free-surface boundary conditions are solved using the finite volume numerical scheme. We examine the effect of varying plug propagation speed and plug length in both the Stokes flow limit and for finite Reynolds number (Re). For a fixed plug length, the trailing film thickness increases with plug propagation speed. If the plug length is greater than the channel width, the trailing film thickness agrees with previous theori

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29

Román, Krishna, Andy Cumbicus, Saba Infante, and Rigoberto Fonseca-Delgado. "Deep Gaussian processes and infinite neural networks for the analysis of EEG signals in Alzheimer’s diseases." Revista de Matemática: Teoría y Aplicaciones 29, no. 2 (2022): 289–312. http://dx.doi.org/10.15517/rmta.v29i2.48885.

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Deep neural network models (DGPs) can be represented hierarchically by a sequential composition of layers. When the prior distribution over the weights and biases are independently identically distributed, there is an equivalence with Gaussian processes (GP) in the limit of an infinite net[1]work width. DGPs are non-parametric statistical models used to character[1]ize patterns of complex non-linear systems due to their flexibility, greater generalization capacity, and a natural way of making inferences about the parameters and states of the system. This article proposes a hierarchi[1]cal Baye

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DELLAR, PAUL J. "Planar channel flow in Braginskii magnetohydrodynamics." Journal of Fluid Mechanics 667 (January 14, 2011): 520–43. http://dx.doi.org/10.1017/s0022112010004507.

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Braginskii magnetohydrodynamics (MHD) is a single-fluid description of large-scale motions in strongly magnetised plasmas. The ion Larmor radius in these plasmas is much shorter than the mean free path between collisions, so momentum transport across magnetic field lines is strongly suppressed. The relation between the strain rate and the viscous stress becomes highly anisotropic, with the viscous stress being predominantly aligned parallel to the magnetic field. We present an analytical study of the steady planar flow across an imposed uniform magnetic field driven by a uniform pressure gradi

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Yariv, Ehud, and John D. Sherwood. "Application of Schwarz–Christoffel mapping to the analysis of conduction through a slot." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2181 (2015): 20150292. http://dx.doi.org/10.1098/rspa.2015.0292.

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We consider the generic problem of steady conduction through a slot traversing a non-conducting plate that separates two semi-infinite conducting regions. The current-density field is conservative; the dimensionless problem governing its potential depends upon a single geometric parameter, h , the ratio of the slot length (i.e. the plate thickness) to its width. We construct a Schwarz–Christoffel transformation to handle this two-dimensional transport problem. The transformation is expressed in terms of two parameters which are related to h through two implicit equations; in the limit h →0, it

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Dong, Hao, Jean-Baptiste Doc, and Simon Félix. "Directivity of horns mounted in finite enclosures: A multimodal formulation." Journal of the Acoustical Society of America 155, no. 3 (2024): 2270–79. http://dx.doi.org/10.1121/10.0025389.

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The beamwidth is a primary directivity metric for the design of a constant directivity horn. To date, investigations on this property have predominantly been restricted to the half-space radiation or idealized geometries. This paper examines the beamwidth behavior of an axisymmetric horn mounted in a finite cylindrical enclosure by proposing an elegant multimodal solution to the far-field directivity pattern. The variation of beamwidth is examined for the frequency, dimensions of the enclosure, and shape of the horn. At low frequencies, a fitted model is proposed to precisely depict the intrin

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Segadlo, Kai, Bastian Epping, Alexander van Meegen, David Dahmen, Michael Krämer, and Moritz Helias. "Unified field theoretical approach to deep and recurrent neuronal networks." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 10 (2022): 103401. http://dx.doi.org/10.1088/1742-5468/ac8e57.

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Abstract Understanding capabilities and limitations of different network architectures is of fundamental importance to machine learning. Bayesian inference on Gaussian processes has proven to be a viable approach for studying recurrent and deep networks in the limit of infinite layer width, n → ∞. Here we present a unified and systematic derivation of the mean-field theory for both architectures that starts from first principles by employing established methods from statistical physics of disordered systems. The theory elucidates that while the mean-field equations are different with regard to

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Karakida, Ryo, and Kazuki Osawa. "Understanding approximate Fisher information for fast convergence of natural gradient descent in wide neural networks*." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 12 (2021): 124010. http://dx.doi.org/10.1088/1742-5468/ac3ae3.

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Abstract Natural gradient descent (NGD) helps to accelerate the convergence of gradient descent dynamics, but it requires approximations in large-scale deep neural networks because of its high computational cost. Empirical studies have confirmed that some NGD methods with approximate Fisher information converge sufficiently fast in practice. Nevertheless, it remains unclear from the theoretical perspective why and under what conditions such heuristic approximations work well. In this work, we reveal that, under specific conditions, NGD with approximate Fisher information achieves the same fast

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Wise, Anthony, Chris W. Hughes, and Jeff A. Polton. "Bathymetric Influence on the Coastal Sea Level Response to Ocean Gyres at Western Boundaries." Journal of Physical Oceanography 48, no. 12 (2018): 2949–64. http://dx.doi.org/10.1175/jpo-d-18-0007.1.

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AbstractIt is our aim with this paper to investigate how the presence of a continental shelf and slope alters the relationship between interior ocean dynamics and western boundary (coastal) sea level. The assumption of a flat-bottomed basin with vertical sidewall at the coast is shown to hide the role that depth plays in the net force acting on the coast. A linear β-plane theory is then developed describing the transmission of sea level over variable depth bathymetry as analogous to the steady advection–diffusion of a thermal fluid. The parameter , relating the friction parameter r to the bath

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LEPPINGTON, F. G., and R. A. SISSON. "On the interaction of a moving hollow vortex with an aerofoil, with application to sound generation." Journal of Fluid Mechanics 345 (August 25, 1997): 203–26. http://dx.doi.org/10.1017/s0022112097006253.

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A hollow vortex in the form of a straight tube, parallel to the z-axis, and of radius a, moves in a uniform stream of fluid with velocity U in the x-direction, with U small compared with the sound speed c. This steady flow is disturbed by the presence of a thin symmetric fixed aerofoil. With a change of x-coordinate, the problem is equivalent to that of a moving aerofoil cutting through an initially fixed vortex in still fluid. The aim of this work is to determine the resulting perturbed flow, and to estimate the distant sound field. A detailed calculation is given for the perturbed velocity p

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Lee, J., and J. M. Vanden-Broeck. "Bubbles rising in an inclined two-dimensional tube and jets falling along a wall." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 3 (1998): 332–49. http://dx.doi.org/10.1017/s0334270000009437.

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AbstractThe motion of a two-dimensional bubble rising at a constant velocity U in an inclined tube of width H is considered. The bubble extends downwards without limit, and is bounded on the right by a wall of the tube, and on the left by a free surface. The same flow configuration describes also a jet emerging from a nozzle and falling down along an inclined wall. The acceleration of gravity g and the surface tension T are included in the free surface condition. The problem is characterized by the Froude number the angle β between the left wall and the horizontal, and the angle γ between the

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Ghosh, S., H. C. Chang, and M. Sen. "Heat-transfer enhancement due to slender recirculation and chaotic transport between counter-rotating eccentric cylinders." Journal of Fluid Mechanics 238 (May 1992): 119–54. http://dx.doi.org/10.1017/s0022112092001666.

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Using Stokes flow between eccentric, counter-rotating cylinders as a prototype for bounded, nearly parallel lubrication flow, we investigate the effect of a slender recirculation region within the flow field on cross-stream heat or mass transport in the important limit of high Péclet number Pe where the enhancement over pure conduction heat transfer without recirculation is most pronounced. The steady enhancement is estimated with a matched asymptotic expansion to resolve the diffusive boundary layers at the separatrices which bound the recirculation region. The enhancement over pure conductio

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Волосюк, Валерий Константинович, Семён Сергеевич Жила, Эдуард Алексеевич Цернэ та Александр Иванович Стороженко. "МАТЕМАТИЧЕСКОЕ ОПИСАНИЕ ПРОЦЕДУР ПОСТРОЕНИЯ КОГЕРЕНТНЫХ ИЗОБРАЖЕНИЙ ПРИРОДНЫХ СРЕД В ЗОНЕ ФРАУНГОФЕРА МНОГОКАНАЛЬНЫМИ РАДИОТЕХНИЧЕСКИМИ СИСТЕМАМИ". Aerospace technic and technology, № 4 (14 жовтня 2018): 92–97. http://dx.doi.org/10.32620/aktt.2018.4.11.

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The structure of the electromagnetic field in the domain of its registration is considered in the case of the solution of problems of remote sensing of the underlying surfaces on the basis of the phenomenological approach. This approach is mainly based on the theory of ray optics and the Huygens-Fresnel principle. It allows to determine the radiated and scattered fields for complex types of surfaces. Analysis of the structure of the electromagnetic field shows that it can be regarded as a mathematical transformation over the true image of the surface. In this case, the basic procedures for the

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Copeland, David Watabe. "Fundamental Performance Limits of Heatsinks." Journal of Electronic Packaging 125, no. 2 (2003): 221–25. http://dx.doi.org/10.1115/1.1569262.

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Dedicated fan-duct-heatsink combinations have become a standard means of cooling computer processors. Most previous studies have considered optimization of fin geometry (pitch and thickness) with overall heatsink dimensions (width, height, length) fixed. The present study considers size requirements for the constraints of fixed air volume flow rate and pressure drop, fixed fan/blower power, and fixed thermal conductance. First, an ideal heatsink with infinite fin thermal conductivity is considered, providing simple power-law prediction of performance. Next, fins of finite thermal conductivity

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Raz, Shalom. "Beam stacking: A generalized preprocessing technique." GEOPHYSICS 52, no. 9 (1987): 1199–210. http://dx.doi.org/10.1190/1.1442383.

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Gaussian beams are well understood frequency‐ domain entities combining the directional properties of plane waves with an effectively finite region of support. These outstanding properties are retained not only on a prescribed observation plane, but throughout the propagation path. A preprocessing sequence aimed at transforming raw seismic data into beam stacks is proposed. That is, time‐harmonic Gaussian beams are synthesized, replacing the plane waves generated by conventional slant‐stacking procedures. The suggested scheme is characterized by an open parameter, essentially the beam width, w

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Moukhtari, Fatima-Ezzahra, and Brice Lecampion. "A semi-infinite hydraulic fracture driven by a shear-thinning fluid." Journal of Fluid Mechanics 838 (January 25, 2018): 573–605. http://dx.doi.org/10.1017/jfm.2017.900.

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We use the Carreau rheological model which properly accounts for the shear-thinning behaviour between the low and high shear rate Newtonian limits to investigate the problem of a semi-infinite hydraulic fracture propagating at a constant velocity in an impermeable linearly elastic material. We show that the solution depends on four dimensionless parameters: a dimensionless toughness (function of the fracture velocity, confining stress, material and fluid parameters), a dimensionless transition shear stress (related to both fluid and material behaviour), the fluid shear-thinning index and the r

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Kulyavtseva, Svetlana, and Boris Pevchenko. "TO THE APPLICATION ASSESSMENT OF MASSTRANSFER ANALYTICAL CORRELATIONS TO DEFINE SORPTION CONSTANTS IN SPRM POLYMERIC MATERIALS." Perm National Research Polytechnic University Aerospace Engineering Bulletin, no. 66 (2021): 15–23. http://dx.doi.org/10.15593/2224-9982/2021.66.02.

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The use of analytical solutions for Frick`s diffusion equation to define the main sorption constants leading to the necessity to solve the united problem is shown. To be more exact this is the application assessment of analytical solutions for more often used experimental results and the determination of the representative sample dimensions in the experiments which are need to construct the sorption/desorption curves. By numerical experiments it is established that the most exact values of masstransfer constants are determined for small and middle values of diffuser absorption temporary proces

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Chizat, Lénaïc, Maria Colombo, Xavier Fernández‐Real, and Alessio Figalli. "Infinite‐width limit of deep linear neural networks." Communications on Pure and Applied Mathematics, May 6, 2024. http://dx.doi.org/10.1002/cpa.22200.

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AbstractThis paper studies the infinite‐width limit of deep linear neural networks (NNs) initialized with random parameters. We obtain that, when the number of parameters diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gradient descent on an infinitely wide deterministic linear NN. Moreover, even if the weights remain random, we get their precise law along the training dynamics, and prove a quantitative convergence result of the linear predictor in terms of the number of parameters. We finally study the continuous‐time limit obtained for infinitely

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KHORUNZHY, A., and W. KIRSCH. "Limit of infinite band width for product of two random matrices." Random Operators and Stochastic Equations 5, no. 4 (1997). http://dx.doi.org/10.1515/rose.1997.5.4.325.

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Hanin, Boris. "Random neural networks in the infinite width limit as Gaussian processes." Annals of Applied Probability 33, no. 6A (2023). http://dx.doi.org/10.1214/23-aap1933.

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Demirtas, Mehmet, James Halverson, Anindita Maiti, Matthew D. Schwartz, and Keegan Stoner. "Neural Network Field Theories: Non-Gaussianity, Actions, and Locality." Machine Learning: Science and Technology, December 21, 2023. http://dx.doi.org/10.1088/2632-2153/ad17d3.

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Abstract Both the path integral measure in field theory and ensembles of neural networks describe distributions over functions. When the central limit theorem can be applied in the infinite-width (infinite-$N$) limit, the ensemble of networks corresponds to a free field theory. Although an expansion in $1/N$ corresponds to interactions in the field theory, others, such as in a small breaking of the statistical independence of network parameters, can also lead to interacting theories. These other expansions can be advantageous over the $1/N$-expansion, for example by improved behavior with resp

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Chen, Linxiao, and Joonas Turunen. "Ising Model on Random Triangulations of the Disk: Phase Transition." Communications in Mathematical Physics, December 20, 2022. http://dx.doi.org/10.1007/s00220-022-04508-5.

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AbstractIn Chen and Turunen (Commun Math Phys 374(3):1577–1643, 2020), we have studied the Boltzmann random triangulation of the disk coupled to an Ising model on its faces with Dobrushin boundary condition at its critical temperature. In this paper, we investigate the phase transition of this model by extending our previous results to arbitrary temperature: We compute the partition function of the model at all temperatures, and derive several critical exponents associated with the infinite perimeter limit. We show that the model has a local limit at any temperature, whose properties depend dr

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Sell, Torben, and Sumeetpal Sidhu Singh. "Trace-class Gaussian priors for Bayesian learning of neural networks with MCMC." Journal of the Royal Statistical Society Series B: Statistical Methodology, January 31, 2023. http://dx.doi.org/10.1093/jrsssb/qkac005.

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Abstract This paper introduces a new neural network based prior for real valued functions. Each weight and bias of the neural network has an independent Gaussian prior, with the key novelty that the variances decrease in the width of the network in such a way that the resulting function is well defined in the limit of an infinite width network. We show that the induced posterior over functions is amenable to Monte Carlo sampling using Hilbert space Markov chain Monte Carlo (MCMC) methods. This type of MCMC is stable under mesh refinement, i.e. the acceptance probability does not degenerate as

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Urso, Vittoria, and Lucian A. Constantin. "Quasi-dimensional models applied to kinetic and exchange energy density functionals." European Physical Journal B 94, no. 7 (2021). http://dx.doi.org/10.1140/epjb/s10051-021-00159-y.

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AbstractWe investigate the behavior of three-dimensional 3D exchange energy functional of density-functional theory in anisotropic systems with two-dimensional 2D character and 1D character. The local density approximation (LDA), the generalized gradient approximation (GGA), and the meta-GGA behave as functions of quantum well width. We use the infinite-barrier model (IBM) for the quantum well. In the first section, we describe the problem of three-dimensional exchange functional, in the second section we introduce the quasi-2D IBM system, in the third section we introduce the quasi-1D IBM sys

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