94 research outputs found

    Deep material networks for efficient scale-bridging in thermomechanical simulations of solids

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    We investigate deep material networks (DMN). We lay the mathematical foundation of DMNs and present a novel DMN formulation, which is characterized by a reduced number of degrees of freedom. We present a efficient solution technique for nonlinear DMNs to accelerate complex two-scale simulations with minimal computational effort. A new interpolation technique is presented enabling the consideration of fluctuating microstructure characteristics in macroscopic simulations

    Fredholm integral equations for function approximation and the training of neural networks

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    We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of the first kind by Ritz-Galerkin discretization, Tikhonov regularization and tensor-train methods. Practical application to supervised learning problems of regression and classification type confirm that the resulting algorithms are competitive with state-of-the-art neural network-based methods. Patrick , Aizhan , Ral

    System- and Data-Driven Methods and Algorithms

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    An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

    TRANSMISSION PERFORMANCE OPTIMIZATION IN FIBER-WIRELESS ACCESS NETWORKS USING MACHINE LEARNING TECHNIQUES

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    The objective of this dissertation is to enhance the transmission performance in the fiber-wireless access network through mitigating the vital system limitations of both analog radio over fiber (A-RoF) and digital radio over fiber (D-RoF), with machine learning techniques being systematically implemented. The first thrust is improving the spectral efficiency for the optical transmission in the D-RoF to support the delivery of the massive number of bits from digitized radio signals. Advanced digital modulation schemes like PAM8, discrete multi-tone (DMT), and probabilistic shaping are investigated and implemented, while they may introduce severe nonlinear impairments on the low-cost optical intensity-modulation-direct-detection (IMDD) based D-RoF link with a limited dynamic range. An efficient deep neural network (DNN) equalizer/decoder to mitigate the nonlinear degradation is therefore designed and experimentally verified. Besides, we design a neural network based digital predistortion (DPD) to mitigate the nonlinear impairments from the whole link, which can be integrated into a transmitter with more processing resources and power than a receiver in an access network. Another thrust is to proactively mitigate the complex interferences in radio access networks (RANs). The composition of signals from different licensed systems and unlicensed transmitters creates an unprecedently complex interference environment that cannot be solved by conventional pre-defined network planning. In response to the challenges, a proactive interference avoidance scheme using reinforcement learning is proposed and experimentally verified in a mmWave-over-fiber platform. Except for the external sources, the interference may arise internally from a local transmitter as the self-interference (SI) that occupies the same time and frequency block as the signal of interest (SOI). Different from the conventional subtraction-based SI cancellation scheme, we design an efficient dual-inputs DNN (DI-DNN) based canceller which simultaneously cancels the SI and recovers the SOI.Ph.D

    Bifurcation analysis of the Topp model

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    In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao
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