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Anomaly detection in time-series data using evolutionary neural architecture search with non-differentiable functions

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APPLIED SOFT COMPUTING 2024年 155卷

作者： Gomez-Rosero, Santiago Capretz, Miriam A. M. Western Univ Dept Elect & Comp Engn London ON N6A 3K7 Canada

Deep neural networks have become the benchmark in diverse fields such as energy consumption forecasting, speech recognition, and anomaly detection, owing to their ability to efficiently process and analyse data. However, they face challenges in managing the complexity and variability in time series data, often leading to increased model complexity and prolonged search duration during parameter tuning. This paper proposes a novel anomaly detection approach through evolutionary neural architecture search (AD-ENAS), which is specifically designed for time series data. The proposed approach focuses on the search for the optimal and minimal neural network architecture. The AD-ENAS method consists of two main phases: architecture evolution and weight adjustment. The architecture evolution phase highlights the importance of neural network architecture by evaluating the fitness of each network agent using shared weight values. Subsequently, the convolutional matrix adaptation technique is used in the next phase for optimal weight adjustment of the neural network. The proposed AD-ENAS method operates without relying on differentiable functions, thus expanding the scope of neural network design beyond traditional backpropagation-based approaches. Various non -differentiable loss functions are explored to facilitate effective architecture search and weight adjustment. Comparative experiments are conducted with five baseline anomaly detection methods on three well-known datasets from reputable sources such as NASA SMAP, NASA MSL and Yahoo S5 -A1. The results demonstrate that the AD-ENAS approach effectively evolves neural network architectures, outperforming baseline methods with F1 scores across the three datasets (MSL: 0.942, SMAP: 0.961, Yahoo S5 -A1: 0.988) with non -differentiable loss functions, showcasing its efficacy in detecting anomalies in time series data.

关键词： Evolutionary neural architecture search Anomaly detection Time series data Shared weights Evolution strategies non-differentiable functions

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A mixed pressure-velocity formulation to model flow in heterogeneous porous media with physics-informed neural networks

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ADVANCES IN WATER RESOURCES 2023年 181卷

作者： Lehmann, Francois Fahs, Marwan Alhubail, Ali Hoteit, Hussein Univ Strasbourg Inst Terre & Environm Strasbourg CNRS ENGEES Strasbourg France King Abdullah Univ Sci & Technol Phys Sci & Engn Div Thuwal Saudi Arabia

Current implementations of Physics Informed Neural Networks (PINNs) can experience convergence problems in simulating fluid flow in porous media with highly heterogeneous domains. The objective of this work is to develop an accurate implementation of PINNs to model fluid flow in heterogeneous porous media that avoids alternative approaches in the literature that tend to impose unphysical continuity of the hydraulic conductivity field. The proposed implementation is inspired by the mixed formulation of the governing equations, which separates the mass continuity equation and Darcy's law. This methodology has been used with the mixed finite element method and is known to provide accurate pressure and velocity fields in highly heterogeneous domains. In this work, a similar methodology is applied to PINNs, where the training loss function is based on the decoupled continuity equation and Darcy's law. The separation of the continuity equation and Darcy's law allows for calculating the residual term in the learning loss function without evaluating the spatial derivatives of the discontinuous hydraulic conductivity and associated non-differentiable functions. This approach provides more accurate automatic differentiation of the neural networks for pressure and velocity fields. The new implementation of PINNs can be applied to simulate flow in porous media, regardless of the type and level of heterogeneity with a discontinuous hydraulic conductivity distribution. A variety of structures of the new implementation are investigated. Numerical experiments show that the structure based on different neural networks for the pressure and each component of the velocity field provides the highest accuracy with equivalent training time as other structures. The proposed methodology presents a novel approach to broaden the scope of PINNs in modeling fluid flow in porous media, while preserving the precise representation of the domain's discontinuous features.

关键词： Physics Informed Neural Networks (PINNs) Flow in porous media Heterogeneous domains Mixed formulation Automatic differentiation non-differentiable functions

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A non-monotone Conjugate Subgradient Type Method for Minimization of Convex functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2020年第2期184卷 534-546页

作者： Konnov, Igor Kazan Fed Univ Dept Syst Anal & Informat Technol Ul Kremlevskaya 18 Kazan 420008 Russia

We suggest a conjugate subgradient type method without any line search for minimization of convex non-differentiable functions. Unlike the custom methods of this class, it does not require monotone decrease in the goal function and reduces the implementation cost of each iteration essentially. At the same time, its step-size procedure takes into account behavior of the method along the iteration points. The preliminary results of computational experiments confirm the efficiency of the proposed modification.

关键词： Convex minimization problems non-differentiable functions Conjugate subgradient method Simple step-size choice Convergence properties

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Local generalizations of the derivatives on the real line

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COMMUNICATIONS IN nonLINEAR SCIENCE AND NUMERICAL SIMULATION 2021年 96卷 105576-105576页

作者： Prodanov, Dimiter IMEC Environm Hlth & Safety Kapeldreef 75 B-3001 Leuven Belgium Bulgarian Acad Sci IICT MMSDP Acad G Bonchev St Sofia 1113 Bulgaria

From a physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth as expressed by the Lipschitz condition. On the other hand, non-linear local growth conditions have been also proposed in the literature. The manuscript investigates the general properties of the local generalizations of derivatives assuming the usual topology of the real line. The concept of a derivative is generalized in terms of the local growth condition of the primitive function. These derivatives are called modular derivatives. Furthermore, the conditions of existence of the modular derivatives are established. The conditions for the continuity of the generalized derivative are also demonstrated. Finally, a generalized Taylor-Lagrange property is proven. It is demonstrated that only the Lipschitz condition has the special property that the derivative function is non-trivially continuous so that the derivative does not vanish. (c) 2021 Elsevier B.V. All rights reserved.

关键词： non-differentiable functions Moduli of continuity H?lder classes Lipschitz condition

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non-differentiable Solutions for Local Fractional nonlinear Riccati Differential Equations

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FUNDAMENTA INFORMATICAE 2017年第1-4期151卷 409-417页

作者： Yang, Xiao-Jun Srivastava, H. M. Torres, Delfim F. M. Zhang, Yudong China Univ Min & Technol Sch Mech & Civil Engn Xuzhou 221116 Peoples R China Univ Victoria Dept Math & Stat Victoria BC V8W 3R4 Canada Univ Aveiro Dept Math Ctr Res & Dev Math & Applicat CIDMA P-3810193 Aveiro Portugal Nanjing Normal Univ Sch Comp Sci & Technol Nanjing 210023 Jiangsu Peoples R China China Univ Min & Technol Dept Math & Mech Xuzhou 221008 Peoples R China China Med Univ Taichung 40402 Taiwan

We investigate local fractional nonlinear Riccati differential equations (LFNRDE) by transforming them into local fractional linear ordinary differential equations. The case of LFNRDE with constant coefficients is con... 详细信息

关键词： nonlinear Riccati equations non-differentiable functions local fractional derivatives

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Local fractional variational iteration algorithm II for non-homogeneous model associated with the non-differentiable heat flow

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ADVANCES IN MECHANICAL ENGINEERING 2015年第10期7卷 1-5页

作者： Zhang, Yu Srivastava, Hari M. Baleanu, Mihaela-Cristina North China Univ Water Resources & Elect Power Coll Math & Informat Sci Zhengzhou Peoples R China Univ Victoria Dept Math & Stat Victoria BC Canada Mihail Sadoveanu Theoret High Sch Bucharest 021586 Romania

In this article, we begin with the non-homogeneous model for the non-differentiable heat flow, which is described using the local fractional vector calculus, from the first law of thermodynamics in fractal media point view. We employ the local fractional variational iteration algorithm II to solve the fractal heat equations. The obtained results show the non-differentiable behaviors of temperature fields of fractal heat flow defined on Cantor sets.

关键词： Local fractional variational iteration algorithm II non-homogeneous model heat flow non-differentiable functions local fractional derivative operators

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SOME APPLICATIONS OF FRACTIONAL VELOCITIES

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FRACTIONAL CALCULUS AND APPLIED ANALYSIS 2016年第1期19卷 173-187页

作者： Prodanov, Dimiter IMEC VZW Neurosci Res Flanders Dept Environm Hlth & Safety Kapeldreef 75 B-3001 Leuven Belgium

Fractional velocity is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. The fractional velocity can be suitable for characterizing singular behavior of derivatives of Holderian functions and non differentiable functions. Relations to integer-order derivatives and other integral-based definitions are discussed. It is demonstrated that for Holder functions under certain conditions the product rules deviates from the Leibniz rule. This deviation is expressed by another quantity, fractional co-variation.

关键词： fractional calculus non-differentiable functions singular functions Holder classes pseudodifferential operators

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Generalized Kiesswetter’s functions

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Real Analysis Exchange 2015年第1期40卷 141-156页

作者： Delong Li Jie Miao Department of Mathematics and Statistics Arkansas State University State University AR 72467 USA

In 1966, Kiesswetter found an interesting example of continuous everywhere but differentiable nowhere functions using base-4 expansion of real numbers. In this paper we show how Kiesswetter’s function can be extended... 详细信息

关键词： 26A06 26A27 26A15 continuous functions non-differentiable functions

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FRACTIONAL VARIATION OF HOLDERIAN functions

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FRACTIONAL CALCULUS AND APPLIED ANALYSIS 2015年第3期18卷 580-602页

作者： Prodanov, Dimiter IMEC VZW Dept Environm Hlth & Safety Neurosci Res Flanders B-3001 Louvain Belgium

The paper demonstrates the basic properties of the local fractional variation operators (termed fractal variation operators). The action of the operators is demonstrated for local characterization of Holderian functions. In particular, it is established that a class of such functions exhibits singular behavior under the action of fractal variation operators in infinitesimal limit. The link between the limit of the fractal variation of a function and its derivative is demonstrated. The paper presents a number of examples, including the calculation of the fractional variation of Cauchy sequences leading to the Dirac's delta-function.

关键词： fractional calculus non-differentiable functions singular functions Holder classes pseudodifferential operators

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Vector Resource Allocation Problems in Communication Networks

Vector Resource Allocation Problems in Communication Network...

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11th International Symposium and Workshops on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt)

作者： Konnov, Igor Kashina, Olga Laitinen, Erkki Kazan Fed Univ Dept Syst Anal & Informat Technol Kazan 420008 Russia

ISBN: (纸本)9781612848242

We consider a problem of optimal allocation of a homogeneous resource in spatially distributed systems such as communication networks, where both utilities of users and network expenses must be taken into account. The network is divided into zones which leads to a two-level vector optimization problem and involves non-differentiable functions whose values are computed algorithmically. We propose several approaches to find a solution. Also, new simple subgradient type methods for non-differentiable Pareto optimization problems are suggested. Their performance is illustrated by computational results on test problems.

关键词： Resource allocation spatial systems communication networks multi-objective optimization non-differentiable functions subgradient methods

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