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The predictions from time series data can help us sense development trends and make scientific decisions in advance. The commonly used forecasting methods with backpropagation consume a lot of computational resources. The deep echo state network (DeepESN) is an advanced prediction method with a deep neural network structure and training algorithm without backpropagation. In this paper, a Bayesian optimization algorithm (BOA) is proposed to optimize DeepESN to address the problem of increasing parameter scale. Firstly, the DeepESN was studied and constructed as the basic prediction model for the time series data. Secondly, the BOA was reconstructed, based on the DeepESN, for optimal parameter searching. The algorithm is proposed within the framework of the DeepESN. Thirdly, an experiment was conducted to verify the DeepESN with a BOA within three datasets: simulation data generated from computer programs, a real humidity dataset collected from Beijing, and a power load dataset obtained from America. Compared with the models of BP (backpropagation), LSTM (long short-term memory), GRU (gated recurrent unit), and ESN (echo state network), DeepESN obtained optimal results, which were 0.0719, 18.6707, and 764.5281 using RMSE evaluation. While getting better accuracy, the BOA optimization time was only 323.4 s, 563.2 s, and 9854 s for the three datasets. It is more efficient than grid search and grey wolf optimizer. [ABSTRACT FROM AUTHOR]

Air quality plays a vital role in people's health, and air quality forecasting can assist in decision making for government planning and sustainable development. In contrast, it is challenging to multi-step forecast accurately due to its complex and nonlinear caused by both temporal and spatial dimensions. Deep models, with their ability to model strong nonlinearities, have become the primary methods for air quality forecasting. However, because of the lack of mechanism-based analysis, uninterpretability forecasting makes decisions risky, especially when the government makes decisions. This paper proposes an interpretable variational Bayesian deep learning model with information self-screening for PM2.5 forecasting. Firstly, based on factors related to PM2.5 concentration, e.g., temperature, humidity, wind speed, spatial distribution, etc., an interpretable multivariate data screening structure for PM2.5 forecasting was established to catch as much helpful information as possible. Secondly, the self-screening layer was implanted in the deep learning network to optimize the selection of input variables. Further, following implantation of the screening layer, a variational Bayesian gated recurrent unit (GRU) network was constructed to overcome the complex distribution of PM2.5 and achieve accurate multi-step forecasting. The high accuracy of the proposed method is verified by PM2.5 data in Beijing, China, which provides an effective way, with multiple factors for PM2.5 forecasting determined using deep learning technology. [ABSTRACT FROM AUTHOR]

Accurate traffic congestion estimation and prediction are critical building blocks for smart trip planning and rerouting decisions in transportation systems. Over the decades, there have been many studies focusing on traffic congestion estimation and prediction with different statistical approaches (e.g., Markov chain) and machine learning models (e.g., clustering, Bayesian networks, and artificial neural networks). However, there is a lack of a unified framework to address the mechanisms of different models and integrate the advantages of different methods through combinations. This paper introduces the FD-Markov-LSTM model, a hybrid interpretable approach that combines the fundamental diagram (FD), Markov chain, and long short-term memory (LSTM). The aim is to estimate and predict traffic states by integrating statistical data in both congested and uncongested scenarios. The FD-Markov-LSTM model leverages the FD to identify hierarchical traffic states and utilizes the Markov process to capture the probabilistic transitions between these states. We employ the LSTM model to further capture the residual time series produced by the Markov chain model (assuming a memoryless property) to enhance the estimation and prediction performance. The proposed model's accuracy in estimating and predicting traffic flow is evaluated using empirical data from three case studies conducted in Beijing and Los Angeles. The results highlight a significant improvement in accuracy compared to classical benchmark models such as the Markov model, ARIMA model, k-Nearest Neighbor model, Random Forest model, and LSTM. Specifically, the FD-Markov-LSTM model achieves reductions of over 39% in mean absolute error, 35% in root mean squared error, and 7.4% in mean absolute percentage error. These results clearly demonstrate that the FD-Markov-LSTM model outperforms the benchmark models, enabling more precise predictions of traffic flow. [ABSTRACT FROM AUTHOR]