检索结果-内蒙古大学图书馆

Inferring the Parameters of Ultrafast Lasers from Images with Surface Patterns

学校读者我要写书评

暂无评论

Inferring the Parameters of Ultrafast Lasers from Images wit...

International Symposium on Image and Signal Processing and Analysis

作者： Anastasis Litsas Fotis Fraggelakis George D. Tsibidis Emmanuel Stratakis Yannis Pantazis Computer Science Department University of Crete Heraklion Greece Institute of Electronic Structure and Laser Foundation for Research and Technology - Hellas Heraklion Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology - Hellas Heraklion Greece

In this paper, we explore the potential of deep learning techniques in the field of ultra-fast laser processing. More specifically, we trained convolutional neural networks on an in-house dataset with the aim of predicting the laser parameters from images which capture the morphological characteristics of the material surface after being laser fabricated. There are several challenges related with the collected dataset stemming from stochastic variations of the material and the laser, the sampling scheme and the overall low sample size. Therefore, to further test our models we additionally construct a synthetic dataset. The results on the synthetic dataset are almost perfect showing that the proposed predictive models have the capacity to learn the assigned tasks. As expected, the predictive performance decreases when the real dataset is utilized. Nevertheless, we show that both the accuracy in the classification task and the mean square error in the majority of the regression tasks are satisfactory (e.g., classification accuracy drops from 99.9% to 94.8%).

关键词：

Current-induced second harmonic generation of Dirac or Weyl semimetals in a strong magnetic field

学校读者我要写书评

暂无评论

Physical Review B 2021年第4期103卷 L041301-L041301页

作者： Yang Gao Furu Zhang College of Computer Science and Engineering Anhui University of Science and Technology Huainan 232001 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We theoretically investigate the second harmonic generation (SHG) of Dirac or Weyl semimetals under parallel DC electric and strong magnetic fields using the Boltzmann equation approach. The DC current-induced SHG process originates from the optical intraband transitions of the Landau subbands. It is a remarkable fingerprint of three-dimensional Dirac or Weyl dispersions and absent in other materials. An analytical formula for the SHG tensor is derived, and it shows chirality independence. The second-order nonlinear optical susceptibility is proportional to the DC field, giving strong optical nonlinearity up to 105pm/V with THz light, which is several orders larger than that of the usual materials. More interesting, the second harmonic conductivity is found to exhibit periodicity in magnetic field 1/B oscillations, which are similar to the Shubnikov–de Haas oscillations. Thus our work proposes another approach for SHG and potential applications of Dirac or Weyl semimetals in nonlinear optics.

关键词： Landau levels Nonlinear optical susceptibility Photoconductivity Semimetals Boltzmann theory Optical second-harmonic generation

PIRATENETS: PHYSICS-INFORMED DEEP LEARNING WITH RESIDUAL ADAPTIVE NETWORKS

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Wang, Sifan Li, Bowen Perdikaris, Paris Chen, Yuhan Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mathematics Duke University DurhamNC27708 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States Department of Electrical and Computer Engineering North Carolina State University RaleighNC27695 United States

While physics-informed neural networks (PINNs) have become a popular deep learning framework for tackling forward and inverse problems governed by partial differential equations (PDEs), their performance is known to degrade when larger and deeper neural network architectures are employed. Our study identifies that the root of this counter-intuitive behavior lies in the use of multi-layer perceptron (MLP) architectures with non-suitable initialization schemes, which result in poor trainablity for the network derivatives, and ultimately lead to an unstable minimization of the PDE residual loss. To address this, we introduce Physics-Informed Residual Adaptive Networks (PirateNets), a novel architecture that is designed to facilitate stable and efficient training of deep PINN models. PirateNets leverage a novel adaptive residual connection, which allows the networks to be initialized as shallow networks that progressively deepen during training. We also show that the proposed initialization scheme allows us to encode appropriate inductive biases corresponding to a given PDE system into the network architecture. We provide comprehensive empirical evidence showing that PirateNets are easier to optimize and can gain accuracy from considerably increased depth, ultimately achieving state-of-the-art results across various benchmarks. All code and data accompanying this manuscript will be made publicly available at https://***/PredictiveIntelligenceLab/jaxpi. © 2024, CC BY-NC-ND.

关键词： Inverse problems

Butterfly-Accelerated Solution of Coupled Volume Integral and Hydrodynamic Equations

学校读者我要写书评

暂无评论

Butterfly-Accelerated Solution of Coupled Volume Integral an...

USNC-URSI Radio science Meeting (Joint with AP-S Symposium)

作者： Doolos Aibek Uulu Yang Liu Abdulkadir C. Yucel Hakan Bagci Department of Mathematics and Natural Sciences University of Central Asia (UCA) Naryn Kyrgyzstan Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory Berkeley USA School of Electrical and Electronic Engineering Nanyang Technological University (NTU) Singapore Computer Electrical and Mathematical Science and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia

ISBN: (数字)9789463968119

ISBN: (纸本)9798350359497

In recent years, advancements in plasmonic devices have enabled the localization of electromagnetic fields at subwavelength scales, contributing to breakthroughs in various scientific and engineering fields (J. C. Ndukaife, et al., ACS Nano, 2014,8,9,9035-9043). These structures are often made of metals and their electric properties are typically represented by the classical Drude model (S. A. Maier, 2007, Springer, New York). As the size of the plasmonic structures approaches the nanoscale, the classical Drude model falls short in explaining the collective movement of free electrons in metals. The interaction between moving charges and the electromagnetic fields can be described by a coupled system of the Maxwell and hydrodynamic equations (X. Zheng, et al., IEEE Trans. Antennas Propag., 2018,66,9, 4759-4771).

关键词： Location awareness Conferences Integral equations Metals Plasmons Hydrodynamics Mathematical models

ERROR ANALYSIS FOR DISCONTINUOUS GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS VIA MAXIMAL REGULARITY

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Akrivis, Georgios Larsson, Stig Department of Computer Science and Engineering University of Ioannina Ioannina451 10 Greece Institute of Applied and Computational Mathematics FORTH Heraklion Crete700 13 Greece Department of Mathematical Sciences Chalmers University of Technology University of Gothenburg GothenburgSE–412 96 Sweden

We consider the discretization of a class of nonlinear parabolic equations by discontinuous Galerkin time-stepping methods and establish a priori as well as conditional a posteriori error estimates. Our approach is motivated by the error analysis in [9] for Runge–Kutta methods for nonlinear parabolic equations;in analogy to [9], the proofs are based on maximal regularity properties of discontinuous Galerkin methods for nonautonomous linear parabolic *** Codes 65M12, 65M15, 65M60 © 2024, CC BY.

关键词： Galerkin methods

An Improved Unbiased Particle Filter

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando 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 Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

Expressive probabilistic sampling in recurrent neural networks

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Chen, Shirui Jiang, Linxing Preston Rao, Rajesh P.N. Shea-Brown, Eric Department of Applied Mathematics University of Washington Seattle United States Paul G. Allen School of Computer Science & Engineering University of Washington Seattle United States Center for Neurotechnology University of Washington Seattle United States Department of Applied Mathematics Computational Neuroscience Center University of Washington Seattle United States

In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for recurrent neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples (sampler-only network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits reservoir-sampler networks (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based Bayesian brain models. Copyright © 2023, The Authors. All rights reserved.

关键词： Probability distributions

A SUCCESSIVE TWO-STAGE METHOD FOR SPARSE GENERALIZED EIGENVALUE PROBLEMS

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Li, Qia Liao, Jianmin Shen, Lixin Zhang, Na School of Computer Science and Engineering Guangdong Province Key Laboratory of Computational Science Sun Yat-sen University Guangdong Province Guangzhou510275 China Department of Mathematics Syracuse University SyracuseNY13244 United States Department of Applied Mathematics College of Mathematics and Informatics South China Agricultural University Guangdong Province Guangzhou510642 China

The Sparse Generalized Eigenvalue Problem (sGEP), a pervasive challenge in statistical learning methods including sparse principal component analysis, sparse Fisher's discriminant analysis, and sparse canonical correlation analysis, presents significant computational complexity due to its NP-hardness. The primary aim of sGEP is to derive a sparse vector approximation of the largest generalized eigenvector, effectively posing this as a sparse optimization problem. Conventional algorithms for sGEP, however, often succumb to local optima and exhibit significant dependency on initial points. This predicament necessitates a more refined approach to avoid local optima and achieve an improved solution in terms of sGEP's objective value, which we address in this paper through a novel successive two-stage method. The first stage of this method incorporates an algorithm for sGEP capable of yielding a stationary point from any initial point. The subsequent stage refines this stationary point by adjusting its support, resulting in a point with an enhanced objective value relative to the original stationary point. This support adjustment is achieved through a novel procedure we have named support alteration. The final point derived from the second stage then serves as the initial point for the algorithm in the first stage, creating a cyclical process that continues until a predetermined stopping criterion is satisfied. We also provide a comprehensive convergence analysis of this process. Through extensive experimentation under various settings, our method has demonstrated significant improvements in the objective value of sGEP compared to existing methodologies, underscoring its potential as a valuable tool in statistical learning and *** Codes 90C26, 90C32, 90C59, 90C90 Copyright © 2023, The Authors. All rights reserved.

关键词： Principal component analysis

A mathematical model with numerical simulations for malaria transmission dynamics with differential susceptibility and partial immunity

学校读者我要写书评

暂无评论

Healthcare Analytics 2023年 3卷 100165-100165页

作者： Tchoumi, S.Y. Rwezaura, H. Tchuenche, J.M. Department of Mathematics and Computer Sciences ENSAI – University of N'Gaoundéré N'Gaoundéré Cameroon Department of Mathematics and Applied Mathematics University of Pretoria South Africa Mathematics Department University of Dar es Salaam Dar es Salaam Tanzania School of Computational and Communication Sciences and Engineering Nelson Mandela African Institution of Science and Technology Arusha Tanzania School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa

Malaria is a deadly vector-borne infectious disease with high prevalence in the world's endemic tropical and subtropical regions. Differences in individuals’ disease susceptibility may lead to their differentiation of susceptibility to infection. We formulate a mathematical model for malaria transmission dynamics that accounts for the host's differential susceptibility, where partial immunity is acquired after infection. As customary, the explicit formula for the basic reproduction number is derived and used to determine the local stability of the model's equilibria. An analysis of a special case with two susceptible classes shows that the model could have two endemic equilibria when the disease threshold parameter is less than unity. Numerical simulations are provided for a differential susceptibility when individuals are re-infected seven times after the initial infection. Graphical representations show that the transient transmission dynamics of the infected components are indistinguishable when there is no inflow into the susceptible classes. When there is an inflow into the various susceptible classes, the graphs of the infected component of the model are fundamentally different, showing that individuals who have been infected multiple times tend to be less infected over time. Knowledge of the inflow rate and the infection reduction rate due to prior infection in each class could be key drivers to mitigate the burden of malaria in a community. © 2023 The Author(s)

关键词： Basic reproduction number Differential susceptibility Immunity Malaria Mathematical modeling Numerical simulation