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Non-Markovian Dynamics: The Governing Equations Of Probability Density Functions for Nonlinear Dynamical systems with Combined Fractional Gaussian and Gaussian White Noises

SSRN

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SSRN 2024年

作者： Pei, Bin Feng, Lifang Li, Yunzhang Xu, Yong School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710072 China Research & Development Institute Northwestern Polytechnical University in Shenzhen Shenzhen518057 China Research Institute of Intelligent Complex Systems Fudan University Shanghai200433 China MOE Key Laboratory for Complexity Science in Aerospace Northwestern Polytechnical University Xi’an710072 China

This paper aims to investigate the non-Markovian dynamics. The governing equations are derived for probability density functions (PDFs) of non-Markovian stochastic responses to nonlinear dynamical systems (NDSs) excited by combined fractional Gaussian noises (FGNs) and Gaussian white noises (GWNs). The main difficulty here, is that, NDSs excited by FGNs cannot be augmented by filters excited by GWNs, leading to the inapplicability of It\^o stochastic calculus theory. Thus, in the present work, based on fractional Wick Itô Skorohod integral and rough path theory, new non-Markovian probability density evolution methods (PDEMs) are established to derive theoretically the fractional-power time varying term-dependent governing equations (FPTV-GEs) for PDFs of non-Markovian stochastic responses to NDSs excited by FGNs and GWNs, which is a breakthrough to stochastic dynamics. Then, we extend an efficient algorithm, the local discontinuous Galerkin method, to numerically solve the FPTV-GEs. Remarkably, this proposed method attains a higher accuracy compared to the prevalent methods such as finite difference, path integral and Monte Carlo methods, and boasts a broader applicability than the path integral method, which fails to solve the FPTV-GEs for PDFs of non-Markovian stochastic responses. Finally, several numerical examples are illustrated to verify the proposed scheme. © 2024, The Authors. All rights reserved.

关键词： Probability density function

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Generative Adversarial Network Based NDVI Super-resolution Reconstruction

Generative Adversarial Network Based NDVI Super-resolution R...

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IEEE Global Conference on Consumer Electronics (GCCE)

作者： Zhengbao Sun Hongyu Pan Kun Yue School of Engineering Yunnan University Kunming China Aerospace Information Reasearch Institute Chinese Academy of Sciences Beijing China School of Information Science and Engineering Yunnan University Kunming China Yunnan Key Laboratory of Intelligent Systems and Computing Yunnan University Kunming China

Low resolution satellite remote sensing images remains a challenge for obtaining high-precision Normalized Difference Vegetation Index (NDVI), and contain some important vegetation cover information for supporting environmental analyses of the surface in large-scale regions, since high-resolution satellite remote sensing observations are still incomplete nowadays. In this paper, we consider the spatial resolution and time series characteristics of remote sensing images, and propose a super-resolution reconstruction algorithm for NDVI fused with Time features by optimizing the Super-Resolution Generative Adversarial Network (TSRGAN). Empirical research in the Salween River estuary area shows that the proposed approach has performance significant advantages in terms of PSNR and SSIM.

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EventHDR: from Event to High-Speed HDR Videos and Beyond

arXiv

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arXiv 2024年

作者： Zou, Yunhao Fu, Ying Takatani, Tsuyoshi Zheng, Yinqiang MIIT Key Laboratory of Complex-field Intelligent Sensing Beijing Institute of Technology Beijing China School of Computer Science and Technology Beijing Institute of Technology Beijing China Institute of Systems and Information Engineering The University of Tsukuba Tsukuba Japan Next Generation Artificial Intelligence Research Center The University of Tokyo Tokyo113-8656 Japan

Event cameras are innovative neuromorphic sensors that asynchronously capture the scene dynamics. Due to the event-triggering mechanism, such cameras record event streams with much shorter response latency and higher intensity sensitivity compared to conventional cameras. On the basis of these features, previous works have attempted to reconstruct high dynamic range (HDR) videos from events, but have either suffered from unrealistic artifacts or failed to provide sufficiently high frame rates. In this paper, we present a recurrent convolutional neural network that reconstruct high-speed HDR videos from event sequences, with a key frame guidance to prevent potential error accumulation caused by the sparse event data. Additionally, to address the problem of severely limited real dataset, we develop a new optical system to collect a real-world dataset with paired high-speed HDR videos and event streams, facilitating future research in this field. Our dataset provides the first real paired dataset for event-to-HDR reconstruction, avoiding potential inaccuracies from simulation strategies. Experimental results demonstrate that our method can generate high-quality, high-speed HDR videos. We further explore the potential of our work in cross-camera reconstruction and downstream computer vision tasks, including object detection, panoramic segmentation, optical flow estimation, and monocular depth estimation under HDR scenarios. © 2024, CC BY.

关键词： Convolutional neural networks

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Averaging principle for semilinear slow-fast rough partial differential equations

arXiv

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arXiv 2024年

作者： Li, Miaomiao Li, Yunzhang Pei, Bin Xu, Yong School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710072 China Research Institute of Intelligent Complex Systems Fudan University Shanghai200433 China Research and Development Institute Northwestern Polytechnical University in Shenzhen Shenzhen518057 China MOE Key Laboratory of Complexity Science in Aerospace Northwestern Polytechnical University Xi’an710072 China

In this paper, we investigate the averaging principle for a class of semilinear slow-fast stochastic partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random rough path, while the fast component is driven by a Brownian rough path. Using controlled rough path theory and the classical Khasminskii’s time discretization scheme, we demonstrate that the slow component converges strongly to the solution of the corresponding averaged equation under the Hölder topology. © 2024, CC BY.

关键词： Stochastic systems

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Non-Markovian dynamics: the memory-dependent probability density evolution equations

arXiv

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arXiv 2024年

This paper aims to investigate the non-Markovian dynamics. The governing equations are derived for the probability density functions (PDFs) of non-Markovian stochastic responses to Langevin equation excited by combined fractional Gaussian noise (FGN) and Gaussian white noise (GWN). The main difficulty here is that the Langevin equation excited by FGN cannot be augmented by a filter excited by GWN, leading to the inapplicability of Itô stochastic calculus theory. Thus, in the present work, based on the fractional Wick Itô Skorohod integral and rough path theory, a new non-Markovian probability density evolution method is established to derive theoretically the memory-dependent probability density evolution equation (PDEEs) for the PDFs of non-Markovian stochastic responses to Langevin equation excited by combined FGN and GWN, which is a breakthrough to stochastic dynamics. Then, we extend an efficient algorithm, the local discontinuous Galerkin method, to numerically solve the memory-dependent PDEEs. Remarkably, this proposed method attains a higher accuracy compared to the prevalent methods such as finite difference, path integral (PI) and Monte Carlo methods, and boasts a broader applicability than the PI method, which fails to solve the memory-dependent PDEEs. Finally, several numerical examples are illustrated to verify the proposed scheme. © 2024, CC BY.

关键词： Stochastic systems

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From Fourier to Neural ODEs: Flow matching for modeling complex systems

arXiv

引用

arXiv 2024年

作者： Li, Xin Zhang, Jingdong Zhu, Qunxi Zhao, Chengli Zhang, Xue Duan, Xiaojun Lin, Wei College of Science National University of Defense Technology Hunan Changsha410073 China School of Mathematical Sciences LMNS SCMS Fudan University China Research Institute of Intelligent Complex Systems Fudan University China State Key Laboratory of Medical Neurobiology MOE Frontiers Center for Brain Science Institutes of Brain Science Fudan University China Shanghai Artificial Intelligence Laboratory China

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a simulation-free framework, called Fourier NODEs (FNODEs), that effectively trains NODEs by directly matching the target vector field based on Fourier analysis. Specifically, we employ the Fourier analysis to estimate temporal and potential high-order spatial gradients from noisy observational data. We then incorporate the estimated spatial gradients as additional inputs to a neural network. Furthermore, we utilize the estimated temporal gradient as the optimization objective for the output of the neural network. Later, the trained neural network generates more data points through an ODE solver without participating in the computational graph, facilitating more accurate estimations of gradients based on Fourier analysis. These two steps form a positive feedback loop, enabling accurate dynamics modeling in our framework. Consequently, our approach outperforms state-of-the-art methods in terms of training time, dynamics prediction, and robustness. Finally, we demonstrate the superior performance of our framework using a number of representative complex systems. © 2024, CC BY.

关键词： Fourier analysis

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Nonlinear Delay-control of Hopf Bifurcation and Stability Switches in a Generlized Logistic Model

Nonlinear Delay-control of Hopf Bifurcation and Stability Sw...

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International Conference on Network and Information systems for Computers (ICNISC)

作者： Shunyi Li School of Mathematics and Statistics Qiannan Normal University for Nationalities Guizhou P.R. China Key Laboratory of Complex Systems and Intelligent Optimization of Guizhou Duyun Guizhou P.R. China

ISBN: (纸本)9781665453523

A generlized Logistic model with nonlinear delayed harvest controlling is considered. The conditions for the stability and local Hopf bifurcation of the equilibrium point are obtained. Numerical examples show that our control strategy can not only control the Hopf bifurcation of the system, but also control the stability switches phenomenon. These are all very useful for the survival of the population.

关键词： Vibrations Sociology Switches Bifurcation Control systems Stability analysis Numerical models

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Long and Short-Term Constraints Driven Safe Reinforcement Learning for Autonomous Driving

arXiv

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arXiv 2024年

作者： Hu, Xuemin Chen, Pan Wen, Yijun Tang, Bo Chen, Long School of Artificial Intelligence Hubei University Wuhan430062 China Key Laboratory of Intelligent Sensing System and Security Hubei University Ministry of Education Hubei Wuhan430062 China Department of Electrical and Computer Engineering Worcester Polytechnic Institute WorcesterMA01609 United States State Key Laboratory of Multimodal Artificial Intelligence Systems State Key Laboratory of Management and Control for Complex Systems Chinese Academy of Sciences Beijing100190 China WAYTOUS Inc. Beijing100083 China Shenzhen518107 China Institute of Artificial Intelligence and Robotics Xi'an Jiaotong University Xi’an710049 China

Reinforcement learning (RL) has been widely used in decision-making and control tasks, but the risk is very high for the agent in the training process due to the requirements of interaction with the environment, which seriously limits its industrial applications such as autonomous driving systems. Safe RL methods are developed to handle this issue by constraining the expected safety violation costs as a training objective, but the occurring probability of an unsafe state is still high, which is unacceptable in autonomous driving tasks. Moreover, these methods are difficult to achieve a balance between the cost and return expectations, which leads to learning performance degradation for the algorithms. In this paper, we propose a novel algorithm based on the long and short-term constraints (LSTC) for safe RL. The short-term constraint aims to enhance the shortterm state safety that the vehicle explores, while the long-term constraint enhances the overall safety of the vehicle throughout the decision-making process, both of which are jointly used to enhance the vehicle safety in the training process. In addition, we develop a safe RL method with dual-constraint optimization based on the Lagrange multiplier to optimize the training process for end-to-end autonomous driving. Comprehensive experiments were conducted on the MetaDrive simulator. Experimental results demonstrate that the proposed method achieves higher safety in continuous state and action tasks, and exhibits higher exploration performance in long-distance decision-making tasks compared with state-of-the-art methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

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Short - Term Prediction of Coke Pushing Current Peak Based on Improved ARIMA Model

Short - Term Prediction of Coke Pushing Current Peak Based o...

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Industrial Cyber-Physical systems (ICPS)

作者： Haiyang Wei Luefeng Chen Jie Hu Yi Ren Min Wu Witold Pedrycz Kaoru Hirota School of Automation China University of Geosciences Wuhan China Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems Wuhan China Engineering Research Center of Intelligent Technology for Geo-Exploration Ministry of Education Wuhan China Department of Electrical and Computer Engineering University of Alberta Edmonton Canada Tokyo Institute of Technology Yokohama Japan

Coke pushing current is an indicator to evaluate the difficulty of coke pushing operation. The higher coke pushing current is, the greater coke pushing resistance is, and the more difficult coke is to push out. Accurate prediction of current peak during future coke pushing operation can provide more time for production personnel to adjust production status and avoid difficult coke pushing in carbonization chamber. In this paper, a combination prediction model based on VMD (Variational Mode Decomposition) and improved ARIMA (Autoregressive Integrated Moving Average) models is proposed. Firstly, VMD algorithm is used to decompose time series of coke pushing current peak, de-noising data, and extracting main information of time series. Then, ARIMA model is used to predict mean change of linear elasticity and GARCH (Generalized Autore-gressive Conditional Heteroskedasticity) model is introduced to predict ARIMA model residual and improve heteroscedasticity of nonlinear part of time series, and then ARIMA-GARCH model is established. Finally, predicted value is obtained by the sum of each component prediction. The experimental results show that the proposed prediction model has a high prediction accuracy in the short-term prediction of coke pushing current peak. The scheme is applied to actual coking production to guide production of coke.

关键词： Resistance Ovens Time series analysis Noise reduction Production Predictive models Prediction algorithms

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Harmonic Disturbance Suppression for High-Performance Nonlinear Repetitive-Control systems

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IFAC-PapersOnLine 2023年第2期56卷 4545-4550页

作者： Shengnan Tian Kang-Zhi Liu Manli Zhang Chengda Lu Min Wu Jinhua She School of Automation China University of Geosciences Wuhan 430074 China. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems Wuhan 430074 China Engineering Research Center of Intelligent Technology for Geo-Exploration Ministry of Education Wuhan 430074 China Department of Electrical and Electronic Engineering Chiba University Chiba 263-8522 Japan School of Engineering Tokyo University of Technology Hachioji Tokyo 192-0982 Japan

This study focuses on the performance design issue of nonlinear repetitive control (RC) systems subject to harmonic disturbances. First, a Takagi-Sugeno fuzzy model is used to describe a nonlinear plant. Then, a repetitive controller featuring a harmonic disturbance period is integrated with an EID estimator to form an RC-EID structure. The structure has a learning feature that gradually reduces the harmonic disturbance estimation error by self-learning. The linear inequality matrices guarantee the stability of nonlinear RC systems. A case study with two permanent magnet synchronous motors shows that the presented RC-EID estimator enhances the harmonic disturbance-suppression performance while compensating for the phase lag caused by the conventional EID filter.

关键词： Nonlinear repetitive control systems harmonic disturbance suppression equivalent input disturbance performance enhancement

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