检索结果-南通市图书馆

Frame Invariance and scalability of Neural Operators for Partial Differential Equations

在线全文

学校读者我要写书评

暂无评论

Communications in Computational Physics 2022年第7期32卷 336-363页

作者： Muhammad I.Zafar Jiequn Han Xu-Hui Zhou Heng Xiao Kevin T.Crofton Department of Aerospace and Ocean Engineering Virginia TechBlacksburgVirginiaUSA Center for ComputationalMathematics Flatiron InstituteNew YorkUSA

Partial differential equations(PDEs)play a dominant role in themathematicalmodeling ofmany complex dynamical *** these PDEs often requires prohibitively high computational costs,especially when multiple evaluations must be made for different parameters or *** training,neural operators can provide PDEs solutions significantly faster than traditional PDE *** this work,invariance properties and computational complexity of two neural operators are examined for transport PDE of a scalar *** operator based on graph kernel network(GKN)operates on graph-structured data to incorporate nonlocal *** we propose a modified formulation of GKN to achieve frame *** cloud neural network(VCNN)is an alternate neural operator with embedded frame invariance which operates on point cloud ***-based neural operator demonstrates slightly better predictive performance compared to ***,GKN requires an excessively high computational cost that increases quadratically with the increasing number of discretized objects as compared to a linear increase for VCNN.

关键词： Neural operators graph neural networks constitutive modeling inverse modeling deep learning

Multi-dimensional band structure spectroscopy in the synthetic frequency dimension

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Light(science & Applications) 2023年第7期12卷 1425-1433页

作者： Dali Cheng Eran Lustig Kai Wang shanhui Fan Ginzton Laboratory and Department of Electrical Engineering Stanford UniversityStanfordCA94305USA Department of Physics McGll UniversityMontrealQC H3A 2T8Canada

The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional *** of these physics are characterized by band structures in more than one *** efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either onedimensional Brillouin zones or one-dimensional subsets of multi-dimensional Billouin *** we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency *** use a single photonic resonator under dynamical modulation to create a multidimensional synthetic frequency *** show that the band structure of such a lattice over the entire multidimensional Brillouin zone can be measured by introducing a gauge potential into the lattice *** this method,we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian *** measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one *** results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension.

关键词： resonator synthetic dimensional

A dive into spectral inference networks: improved algorithms for self-supervised learning of continuous spectral representations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 2023年第7期44卷 1199-1224页

作者： J.Wu s.F.WANG P.PERDIKARIs Graduate Group in Applied Mathematics and Computational science University of Pennsylvania PhiladelphiaPA 19104U.S.A. Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA 19104U.S.A.

We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint *** represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency *** formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the ***,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of *** effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video *** results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.

关键词： spectral learning partial differential equation(PDE) neural network slow features analysis

Hierarchical Mean-Field Type Control of Price Dynamics for Electricity in smart Grid

在线全文

学校读者我要写书评

暂无评论

Journal of systems science & Complexity 2022年第1期35卷 1-17页

作者： FRIHI Zahrate El Oula CHOuTRI salah Eddine BARREIRO-GOMEZ Julian TEMBINE Hamidou Laboratory of Probability and statistics(La Ps) Department of MathematicsBadji-Mokhtar UniversityB.P.12Annaba 23000Algeria. NYuAD Research Institute New York University Abu DhabiUAE Learning&Game Theory Laboratory New York University Abu DhabiSaadiyat Campus PO Box 129188UAE

This paper solves a mean-field type hierarchical optimal control problem in electricity *** authors consider n-1 prosumers and one *** ith prosumer,for 1s a leader of the(i-1)th prosumer and is a follower of the(i+1)th *** first player(agent)is the follower at the bottom whereas the nth is the leader at the *** problem is described by a linear jump-diffusion system of conditional mean-field type,where the conditioning is with respect to common noise,and a quadratic cost functional involving,the square of the conditional expectation of the controls of the *** authors provide a semi-explicit solution of the corresponding meanfield-type hierarchical control problem with common ***,the authors illustrate the obtained result via a numerical example with two different scenarios.

关键词： Electricity price dynamics hierarchical control mean-field-type control smart grids

Flexible atomic buckling and homogeneous edge states in few-layer Bi(110)films

在线全文

学校读者我要写书评

暂无评论

Nano Research 2022年第3期15卷 2374-2381页

作者： Yanfeng Lyu samira Daneshmandi shuyuan Huyan Chingwu Chu Department of Physics and Texas Center for superconductivity University of HoustonHoustonTexas 77204USA Lawrence Berkeley National Laboratory BerkeleyCalifornia 94720USA

The structure and edge states of two-dimensional few-layer Bi(110)films grown on a graphene/siC substrate were studied by low-temperature scanning tunneling microscopy and *** found that the local density of states of few-layer Bi(110)films are layer-dependent and that the films transition from exhibiting semiconducting characteristics to metallic ones as the number of layers *** in-plane lattice structure has numerous displacements and inversions,which implies that the atomic arrangement and atomic buckling in ultrathin Bi(110)films are *** edges formed between 4-monolayer Bi(110)and graphene are reconstructed and distorted,and the corresponding edge states are topographically *** from the substrate and domain boundaries also modify the electronic structures and induce additional defect-dependent *** also found that the zigzag-shaped step edges in few-layer Bi(110)films are nonreconstructed and possess layer-dependent homogeneous edge states,providing a very likely platform for further research on quantum interference of the edge mode in order to confirm the topology in Bi(110).

关键词： few-layer Bi(110)films lattice displacement and inversion distortion zigzag edge edge states

Dynamic nitrogen vacancy magnetometry by single-shot optical streaking microscopy

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Photonics Research 2022年第9期10卷 2147-2156页

作者： MARK A.KEPPLER ZACHARY A.sTEELMAN ZACHARY N.COKER MILOŠNEsLÁDEK PHILIP R.HEMMER VLADIsLAV V.YAKOVLEV JOEL N.BIXLER Department of Biomedical Engineering Texas A&M UniversityCollege StationTexas 77843USA sAIC JBSA Fort Sam HoustonTexas 78234USA National Research Council Research Associateship Program WashingtonDC 20001USA IMOMEC Division IMECB-3590 DiepenbeekBelgium Institute for Materials Research(IMO) Hasselt UniversityB-3590 DiepenbeekBelgium Czech Technical university in Prague 27201 KladnoCzech Republic Department of Electrical and Computer Engineering Texas A&M UniversityCollege StationTexas 77843USA Bioeffects Division Airman System DirectorateAir Force Research LaboratoryJBSA Fort Sam HoustonTexas 78234USA

Nitrogen vacancy diamonds have emerged as sensitive solid-state magnetic field sensors capable of producing diffraction limited and sub-diffraction field ***,for the first time,to our knowledge,we extend those measurements to high-speed imaging,which can be readily applied to analyze currents and magnetic field dynamics in circuits on a microscopic *** overcome detector acquisition rate limitations,we designed an optical streaking nitrogen vacancy microscope to acquire two-dimensional spatiotemporal *** demonstrate magnetic field wave imaging with micro-scale spatial extent and~400μs temporal *** validating this system,we detected magnetic fields down to 10μT for 40 Hz magnetic fields using single-shot imaging and captured the spatial transit of an electromagnetic needle at streak rates as high as 110μm/*** design has the capability to be readily extended to full 3D video acquisition by utilizing compressed sensing techniques and a potential for further improvement of spatial resolution,acquisition speed,and *** device opens opportunities to many potential applications where transient magnetic events can be isolated to a single spatial axis,such as acquiring spatially propagating action potentials for brain imaging and remotely interrogating integrated circuits.

关键词： vacancy utilizing overcome

PDE Constrained Optimization and Design of Frozen Mode Crystals

在线全文

学校读者我要写书评

暂无评论

Communications in Computational Physics 2008年第4期3卷 878-898页

作者： s.Chun J.s.Hesthaven Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA.

We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode *** is characterized by Van Hove singularities in the dispersion relation,e.g.,stationary reflection points and degenerate band edge ***,the optimization process modifies the dispersion relation by adjusting the geometries and material *** resulting algorithm is found to be capable of recovering all known crystal configurations as well as many new configurations,some of which display dramatically improved properties over previously used *** investigate both gyrotropic photonic crystals and degenerate band edge crystals as well as the more complex case of the oblique *** this latter case,we extend the investigation to the three-dimensional case to identify the first three-dimensional crystal exhibiting frozen mode behavior.

关键词： PDE constrained optimization method of matched asymptotics frozen mode photonic crystal.

Dynamic Evasion-Interrogation Games with uncertainty in the Context of Electromagetics

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Numerical Mathematics(Theory,Methods and Applications) 2011年第3期4卷 359-378页

作者： H.T.Banks shuhua Hu K.Ito sarah Grove Muccio Center for Research in scientific Computation North Carolina State UniversityRaleighNC 27695-8212USA.

We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their *** this paper,the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the *** problem is formulated in two different ways;one is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck *** other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov *** addition,a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.

关键词： Electromagnetic evasion-pursuit uncertainty feedback control computational methods Kolmogorov and Fokker-Planck equations.

Modeling of the Frozen Mode Phenomenon and its sensitivity using Discontinuous Galerkin Methods

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2007年第4期2卷 611-639页

作者： s.Chun J.s.Hesthaven Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA.

We investigate the behavior and sensitivity of the frozen mode phenomenon in finite structures with anisotropic materials,including both magnetic materials and non-normal *** studies are done by using a high-order accurate discontinuous Galerkin method for solving Maxwells equations in the time *** confirm the existence of the phenomenon also in the time-domain and study carefully the impact of the finite crystal on the frozen *** sets the stage for a thorough study of the robustness of the frozen mode phenomenon,resulting in guidelines for which design parameters are most sensitive and acceptable tolerances.

关键词： Discontinuous Galerkin method Maxwell equation photonic crystals frozen mode.