449 research outputs found

    Data-driven Discovery of Multiple-Physics Electromagnetic Partial Differential Equations

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    The subject of data-driven discovery for equations has developed rapidly in recent years, especially in the field of finding equations of unknown forms, which provides new ideas for the study of complex systems. When there are unknown noise sources and other uncertain factors in the system, it is quite difficult to directly derive the system governing equation, because the equation is complicated and the calculation cost is large. But if we try to find the equation directly from the data, it will be helpful to improve these problems. For the data in nonlinear multi-physics electromagnetic system, the deep learning method can be used to find the equation, which can obtain the governing equation form accurately and has high time efficiency and parameter precision. This thesis studies the algorithm of data-driven discovery equations in electromagnetic multiple physics problems and realizes the inversion of Maxwell's multiple physics equations. Firstly, three methods of data-driven equation discovery are introduced, including symbol regression, sparse regression and neural network. Secondly, an algorithm based on sparse regression and convolutional neural network is proposed for multiple physics equations of Maxwell equations. This algorithm uses Euler method to approximate time differentiation and convolution kernel to compute space differentiation. At the same time, in the training process, the pareto analysis method was used to remove the redundancy. Then, the model algorithm is applied to the multi-physics coupling simulation data of electromagnetic plasma, and the homogeneous and non-homogeneous equations of electromagnetic propagation are realized by using less time and space observation field samples, which has certain anti-noise performance. For the problem of propagation in uniform medium, the influence of spatial and temporal sampling method on the inversion precision of equation coefficients is studied. Under the condition of inhomogeneous media propagation, this thesis finds the changing law of inhomogeneous coefficient by changing the weight scale of neural network, aiming at the problem that the equation coefficient varies with the spatial scale. By using the properties of trigonometric series and some prior knowledge, the expression of the coefficient of inhomogeneous terms is approximated, and satisfactory results are obtained. Finally, the thesis summarizes the proposed method and its main conclusion. In both homogeneous and inhomogeneous media, the model has good performance. Meanwhile, the author discusses the possible improvement methods for other problems and the idea that the structure of the model can be adjusted in a small range in the future and applied to the high-dimensional space and the problems with high-order spatial differentiation in the governing equations

    Residual Tensor Train: A Quantum-inspired Approach for Learning Multiple Multilinear Correlations

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    States of quantum many-body systems are defined in a high-dimensional Hilbert space, where rich and complex interactions among subsystems can be modelled. In machine learning, complex multiple multilinear correlations may also exist within input features. In this paper, we present a quantum-inspired multilinear model, named Residual Tensor Train (ResTT), to capture the multiple multilinear correlations of features, from low to high orders, within a single model. ResTT is able to build a robust decision boundary in a high-dimensional space for solving fitting and classification tasks. In particular, we prove that the fully-connected layer and the Volterra series can be taken as special cases of ResTT. Furthermore, we derive the rule for weight initialization that stabilizes the training of ResTT based on a mean-field analysis. We prove that such a rule is much more relaxed than that of TT, which means ResTT can easily address the vanishing and exploding gradient problem that exists in the existing TT models. Numerical experiments demonstrate that ResTT outperforms the state-of-the-art tensor network and benchmark deep learning models on MNIST and Fashion-MNIST datasets. Moreover, ResTT achieves better performance than other statistical methods on two practical examples with limited data which are known to have complex feature interactions.Comment: 12 pages, 6 figure

    Development of reduced-order models for predicting the plastic deformation of metals employing material knowledge systems.

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    Metal alloys being explored for structural applications exhibit a complex polycrystalline internal structure that intrinsically spans multiple length-scales. Therefore, rational design efforts for such alloys require a multiscale modeling framework capable of adequately incorporating the appropriate physics that control/drive the plastic deformation at the different length scales when modeling the overall plastic response of the alloy. The establishment of the desired multiscale modeling frameworks requires the development of low-computational cost, non-iterative, frameworks capable of accurately localizing the anisotropic plastic response of polycrystalline microstructures. This dissertation addresses the outlined needs by defining suitable extensions to the scale-bridging, data-driven Material Knowledge System Framework. The extensions detailed in the subsequent chapters enabled the first successful implementation of this framework for predicting the plastic response of polycrystalline microstructures caused by any arbitrary periodic boundary condition imposed at the macroscale. The case studies presented in this work demonstrate that the localization models developed using the MKS framework are of low-computational cost and non-iterative. Nevertheless, their predictions are not as accurate as desired. As a result, leveraging the insights obtained from the implementation of this framework to polycrystalline plasticity, this dissertation provides a robust protocol to incorporate deep learning approaches in order to provide better predictions of the local plastic response in polycrystalline RVEs. The final case study performed in this dissertation establishes that the most robust approaches to develop accurate localization reduced-order models capable of accurately predicting the local anisotropic plastic response of polycrystalline microstructures are deep learning approaches such as Convolutional Neural Networks.Ph.D

    Advanced Methods of Power Load Forecasting

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    This reprint introduces advanced prediction models focused on power load forecasting. Models based on artificial intelligence and more traditional approaches are shown, demonstrating the real possibilities of use to improve prediction in this field. Models of LSTM neural networks, LSTM networks with a SESDA architecture, in even LSTM-CNN are used. On the other hand, multiple seasonal Holt-Winters models with discrete seasonality and the application of the Prophet method to demand forecasting are presented. These models are applied in different circumstances and show highly positive results. This reprint is intended for both researchers related to energy management and those related to forecasting, especially power load

    Detection of Small Targets in Sea Clutter Based on RepVGG and Continuous Wavelet Transform

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    Constructing a high-performance target detector under the background of sea clutter is always necessary and important. In this work, we propose a RepVGGA0-CWT detector, where RepVGG is a residual network that gains a high detection accuracy. Different from traditional residual networks, RepVGG keeps an acceptable calculation speed. Giving consideration to both accuracy and speed, the RepVGGA0 is selected among all the variants of RepVGG. Also, continuous wavelet transform (CWT) is employed to extract the radar echoes' time-frequency feature effectively. In the tests, other networks (ResNet50, ResNet18 and AlexNet) and feature extraction methods (short-time Fourier transform (STFT), CWT) are combined to build detectors for comparison. The result of different datasets shows that the RepVGGA0-CWT detector performs better than those detectors in terms of low controllable false alarm rate, high training speed, high inference speed and low memory usage. This RepVGGA0-CWT detector is hardware-friendly and can be applied in real-time scenes for its high inference speed in detection

    Forecasting etfs- price movements using convolutional neural networks - methodology and comparison of industries - focus on industrials etf

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    The aim of this paper is to achieve two goals. Firstly, build and apply a convolutional neural network to make predictions on historical data of the Vanguard Industrials ETF (VIS) in the form of Buy, Hold and Sell signals. Secondly, making comparisons among different indus triesin order to derive potential performance deviations. By using three image encoding tech niques and a randomly generated model for comparison purposes, some promising results have been achieved. Nevertheless, several classic strategies and the market performance could not be beaten, mainly because model predictions for Buy and Sell signals showed weaknesses

    Application of Shallow Neural Networks to Retail Intermittent Demand Time Series

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    Accurate sales predictions are essential for businesses in the fast-moving consumer goods (FMCG) industry. However, their demand forecasts are often unreliable, leading to imprecisions that affect downstream decisions. This dissertation proposes using an artificial neural network to improve intermittent demand forecasting in the retail sector. The research investigates the validity of using unprocessed historical information, eluding hand-crafted features, to learn patterns in intermittent demand data. The experiment tests a selection of shallow neural network architectures that can expedite the time-to-market in comparison to conventional demand forecasting methods. The results demonstrate that organisations that still rely on manual and direct forecasting methods could improve their predicting accuracy and establish a high-performing baseline for future development. The solution also offers an end-to-end systematic forecasting landscape enabling a lift-and-shift and easy transition from design to deployment. A practical implementation should bring about stable and reliable forecasts, resulting in cost savings, improved customer service, and increased profitability. Lastly, the research findings contribute to the broader academic field of forecasting and ML with a seminal proposal that provides insights and opportunities for future research
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