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Existing models encounter bottlenecks in balancing performance and computational efficiency when modeling long sequences. Although the state space model (SSM) has achieved remarkable success in handling long sequence tasks, it still faces the problem of large number of parameters. In order to further improve the efficiency of SSM, we propose a new state space layer based on multiple-input multiple-output SSM, called efficient SSM (eSSM). Our eSSM is built on the convolutional representation of multi-input and multi-input (MIMO) SSM. We propose a variety of effective strategies to improve the computational efficiency. The diagonalization of the system matrix first decouples the original system. Then a fast tensor convolution is proposed based on the fast Fourier transform. In addition, the block diagonalization of the SSM further reduces the model parameters and improves the model flexibility. Extensive experimental results show that the performance of the proposed model on multiple databases matches the performance of state-of-the-art models, such as S4, and is significantly better than Transformers and LSTM. In the model efficiency benchmark, the parameters of eSSM are only 12.89\% of LSTM and 13.24\% of Mamba. The training speed of eSSM is 3.94 times faster than LSTM and 1.35 times faster than Mamba. Code is available at: \href{https://github.com/leonty1/essm}{https://github.com/leonty1/essm}.

Although deep learning-based methods have shown great success in spatiotemporal predictive learning, the framework of those models is designed mainly by intuition. How to make spatiotemporal forecasting with theoretical guarantees is still a challenging issue. In this work, we tackle this problem by applying domain knowledge from the dynamical system to the framework design of deep learning models. An observer theory-guided deep learning architecture, called Spatiotemporal Observer, is designed for predictive learning of high dimensional data. The characteristics of the proposed framework are twofold: firstly, it provides the generalization error bound and convergence guarantee for spatiotemporal prediction; secondly, dynamical regularization is introduced to enable the model to learn system dynamics better during training. Further experimental results show that this framework could capture the spatiotemporal dynamics and make accurate predictions in both one-step-ahead and multi-step-ahead forecasting scenarios., Comment: Under review by IEEE Transactions on Pattern Analysis and Machine Intelligence

Numerous industrial thermal processes and fluid processes can be described by distributed parameter systems (DPSs), wherein many process parameters and variables vary in space and time. Early internal abnormalities in the DPS may develop into uncontrollable thermal failures, causing serious safety incidents. In this study, the multiscale information fusion is proposed for internal abnormality detection and localization of DPSs under different scenarios. We introduce the dissimilarity statistic as a means to identify anomalies for lumped variables, whereas spatial and temporal statistic measures are presented for the anomaly detection for distributed variables. Through appropriate parameter optimization, these statistic functions are integrated into the comprehensive multiscale detection index, which outperforms traditional single-scale detection methods. The proposed multiscale statistic has good physical interpretability from the system disorder degree. Experiments on the internal short circuit (ISC) of a battery system have demonstrated that our proposed method can swiftly identify ISC abnormalities and accurately pinpoint problematic battery cells under various working conditions.

Identification of abnormal source hidden in distributed parameter systems (DPSs) belongs to the category of inverse source problems. It is important in industrial applications but seldom studied. In this paper, we make the first attempt to investigate the abnormal spatio-temporal (S-T) source identification for a class of DPSs. An inverse S-T model for abnormal source identification is developed for the first time. It consists of an adaptive state observer for source identification and an adaptive source estimation algorithm. One major advantage of the proposed inverse S-T model is that only the system output is utilized, without any state measurement. Theoretic analysis is conducted to guarantee the convergence of the estimation error. Finally, the performance of the proposed method is evaluated on a heat transfer rod with an abnormal S-T source., Comment: This paper has been accepted for publication in IEEE Transactions on Systems, Man, and Cybernetics: Systems

The balance between exploration and exploitation is a key problem for reinforcement learning methods, especially for Q-learning. In this paper, a fidelity-based probabilistic Q-learning (FPQL) approach is presented to naturally solve this problem and applied for learning control of quantum systems. In this approach, fidelity is adopted to help direct the learning process and the probability of each action to be selected at a certain state is updated iteratively along with the learning process, which leads to a natural exploration strategy instead of a pointed one with configured parameters. A probabilistic Q-learning (PQL) algorithm is first presented to demonstrate the basic idea of probabilistic action selection. Then the FPQL algorithm is presented for learning control of quantum systems. Two examples (a spin- 1/2 system and a lamda-type atomic system) are demonstrated to test the performance of the FPQL algorithm. The results show that FPQL algorithms attain a better balance between exploration and exploitation, and can also avoid local optimal policies and accelerate the learning process., Comment: 13 pages, 16 figures

An effective modeling method for nonlinear distributed parameter systems (DPSs) is critical for both physical system analysis and industrial engineering. In this Rapid Communication, we propose a novel DPS modeling approach, in which a high-order nonlinear Volterra series is used to separate the time/space variables. With almost no additional computational complexity, the modeling accuracy is improved more than 20 times in average comparing with the traditional method., Comment: 10 figures, 5 pages