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Purpose The purpose of this paper is to propose a new linear-nonlinear data preprocessing-based hybrid model to achieve a more accurate result at a lower cost for wind power forecasting. For this purpose, a decomposed based series-parallel hybrid model (PKF-ARIMA-FMLP) is proposed which can model linear/nonlinear and certain/uncertain patterns in underlying data simultaneously. Design/methodology/approach To design the proposed model at first, underlying data are divided into two categories of linear and nonlinear patterns by the proposed Kalman filter (PKF) technique. Then, the linear patterns are modeled by the linear-fuzzy nonlinear series (LLFN) hybrid models to detect linearity/nonlinearity and certainty/uncertainty in underlying data simultaneously. This step is also repeated for nonlinear decomposed patterns. Therefore, the nonlinear patterns are modeled by the linear-fuzzy nonlinear series (NLFN) hybrid models. Finally, the weight of each component (e.g. KF, LLFN and NLFN) is calculated by the least square algorithm, and then the results are combined in a parallel structure. Then the linear and nonlinear patterns are modeled with the lowest cost and the highest accuracy. Findings The effectiveness and predictive capability of the proposed model are examined and compared with its components, based models, single models, series component combination based hybrid models, parallel component combination based hybrid models and decomposed-based single model. Numerical results show that the proposed linear-nonlinear data preprocessing-based hybrid models have been able to improve the performance of single, hybrid and single decomposed based prediction methods by approximately 66.29%, 52.10% and 38.13% for predicting wind power time series in the test data, respectively. Originality/value The combination of single linear and nonlinear models has expanded due to the theory of the existence of linear and nonlinear patterns simultaneously in real-world data. The main idea of the linear and nonlinear hybridization method is to combine the benefits of these models to identify the linear and nonlinear patterns in the data in series, parallel or series-parallel based models by reducing the limitations of the single model that leads to higher accuracy, more comprehensiveness and less risky predictions. Although the literature shows that the combination of linear and nonlinear models can improve the prediction results by detecting most of the linear and nonlinear patterns in underlying data, the investigation of linear and nonlinear patterns before entering linear and nonlinear models can improve the performance, which in no paper this separation of patterns into two classes of linear and nonlinear is considered. So by this new data preprocessing based method, the modeling error can be reduced and higher accuracy can be achieved at a lower cost.

In power grid dispatching and planning, the accuracy of electricity demand plays a vital role in the safety and economy of the power grid. In view of the problems existing in the current load forecasting of the power grid, a long-term and short-term hybrid model is studied to improve the accuracy and robustness of load forecasting. This project intends to combine the advantages of Seq2Seq model in time series analysis with ARIMA's advantages in stability to effectively solve the supply and demand relationship in long and short cycles. First, considering the nonlinear characteristics of power demand in the power market, a hybrid modeling framework based on optimality is constructed. It is optimized using methods such as genetics and particle swarms. Secondly, the constructed model is empirically analyzed using simulation experiments, and it is found that the constructed method has excellent accuracy on multiple time scales. Especially in the volatile power market environment, it has better robustness and adaptability. After precise data verification, the average error rate of short-term prediction of this model is within 5%, and within 7% in the longer period.

Heatwaves pose a significant threat to environmental sustainability and public health, particularly in vulnerable regions and rapidly growing cities. They cause water shortages, stress on plants, and an overall drying out of landscapes, reducing plant growth—the basis of energy production and the food chain. Accurate heatwave forecasting is crucial for early warning systems, public health interventions, and disaster preparedness strategies, reducing heat-related mortality risk through modeling and evaluation of warnings. However, anticipating heatwave warnings requires handling the daily time series data, which is a large-scale and high-frequency time series data. High-frequency time series data forecasting presents unique challenges due to its inherent complexity and characteristics. Therefore, the study proposes two algorithms to develop Machine-Learning (ML)-based hybrid models as well as seasonal adjusted ML-based hybrid models, which can handle large datasets and reveal complex seasonal patterns. The performance of these developed ML-based hybrid models and seasonal adjusted ML-based hybrid models were compared with other traditional time series, Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing State Space (ETS), and Trigonometric Box-Cox ARMA Trend Seasonal (TBATS) and ML models, Artificial Neural Network (ANN), Support Vector Regression (SVR), Prophet, Random Forest Regression (RFR), and Long Short-Term Memory (LSTM), to forecast heatwave warnings in Rajshahi, one of Bangladesh’s warmest districts, based on 42-year historical daily instances. Our findings indicate that the seasonal adjusted ML-based hybrid model, by integrating the Seasonal-Trend decomposition procedure based on LOESS (STL) approach with different time series and ML models, STL-ARIMA-LSTM, outperformed all other models with MAE (0.8974), MAPE (2.9232), RMSE (1.1794), MASE (0.3814) and ACF1 (0.0026). Hence, our suggested seasonal adjusted ML-based hybrid model, ensures a more accurate forecast and helps to determine the number and days of heatwaves, enabling people to plan ahead and take necessary safety measures before they occur.

Background This study aimed to construct a more accurate model to forecast the incidence of hand, foot, and mouth disease (HFMD) in mainland China from January 2008 to December 2019 and to provide a reference for the surveillance and early warning of HFMD. Methods We collected data on the incidence of HFMD in mainland China between January 2008 and December 2019. The SARIMA, SARIMA-BPNN, and SARIMA-PSO-BPNN hybrid models were used to predict the incidence of HFMD. The prediction performance was compared using the mean absolute error(MAE), mean squared error(MSE), root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation analysis. Results The incidence of HFMD in mainland China from January 2008 to December 2019 showed fluctuating downward trends with clear seasonality and periodicity. The optimal SARIMA model was SARIMA(1,0,1)(2,1,2) [12] , with Akaike information criterion (AIC) and Bayesian Schwarz information criterion (BIC) values of this model were 638.72, 661.02, respectively. The optimal SARIMA-BPNN hybrid model was a 3-layer BPNN neural network with nodes of 1, 10, and 1 in the input, hidden, and output layers, and the R-squared, MAE, and RMSE values were 0.78, 3.30, and 4.15, respectively. For the optimal SARIMA-PSO-BPNN hybrid model, the number of particles is 10, the acceleration coefficients c1 and c2 are both 1, the inertia weight is 1, the probability of change is 0.95, and the values of R-squared, MAE, and RMSE are 0.86, 2.89, and 3.57, respectively. Conclusions Compared with the SARIMA and SARIMA-BPNN hybrid models, the SARIMA-PSO-BPNN model can effectively forecast the change in observed HFMD incidence, which can serve as a reference for the prevention and control of HFMD.

Load forecasting is an essential task in the operation management of a power system. Electric power companies utilize short-term load forecasting (STLF) technology to make reasonable power generation plans. A forecasting model with low prediction errors helps reduce operating costs and risks for the operators. In recent years, machine learning has become one of the most popular technologies for load forecasting. In this paper, a two-stage STLF model based on long short-term memory (LSTM) and multilayer perceptron (MLP), which improves the forecasting accuracy over the entire time horizon, is proposed. In the first stage, a sequence-to-sequence (seq2seq) architecture, which can handle a multi-sequence of input to extract more features of historical data than that of single sequence, is used to make multistep predictions. In the second stage, the MLP is used for residual modification by perceiving other information that the LSTM cannot. To construct the model, we collected the electrical load, calendar, and meteorological records of Kanto region in Japan for four years. Unlike other LSTM-based hybrid architectures, the proposed model uses two independent neural networks instead of making the neural network deeper by concatenating a series of LSTM cells and convolutional neural networks (CNNs). Therefore, the proposed model is easy to be trained and more interpretable. The seq2seq module performs well in the first few hours of the predictions. The MLP inherits the advantage of the seq2seq module and improves the results by feeding artificially selected features both from historical data and information of the target day. Compared to the LSTM-AM model and single MLP model, the mean absolute percentage error (MAPE) of the proposed model decreases from 2.82% and 2.65% to 2%, respectively. The results demonstrate that the MLP helps improve the prediction accuracy of seq2seq module and the proposed model achieves better performance than other popular models. In addition, this paper also reveals the reason why the MLP achieves the improvement.

In various fields, knowledge distillation (KD) techniques that combine vision transformers (ViTs) and convolutional neural networks (CNNs) as a hybrid teacher have shown remarkable results in classification. However, in the realm of remote sensing images (RSIs), existing KD research studies are not only scarce but also lack competitiveness. This issue significantly impedes the deployment of the notable advantages of ViTs and CNNs. To tackle this, the authors introduce a novel hybrid‐model KD approach named HMKD‐Net, which comprises a CNN‐ViT ensemble teacher and a CNN student. Contrary to popular opinion, the authors posit that the sparsity in RSI data distribution limits the effectiveness and efficiency of hybrid‐model knowledge transfer. As a solution, a simple yet innovative method to handle variances during the KD phase is suggested, leading to substantial enhancements in the effectiveness and efficiency of hybrid knowledge transfer. The authors assessed the performance of HMKD‐Net on three RSI datasets. The findings indicate that HMKD‐Net significantly outperforms other cutting‐edge methods while maintaining a significantly smaller size. Specifically, HMKD‐Net exceeds other KD‐based methods with a maximum accuracy improvement of 22.8% across various datasets. As ablation experiments indicated, HMKD‐Net has cut down on time expenses by about 80% in the KD process. This research study validates that the hybrid‐model KD technique can be more effective and efficient if the data distribution sparsity in RSIs is well handled.

A method for computational modeling of rapidly developing biophysical processes on the basis of physical analogies and the transient damped oscillation theory has been developed. The relevant phenomena, including invasions of aggressive species, have been discussed and epidemics in the form of a series of peaks in the pathogen activity have been compared. The spread of COVID waves in regions turned out to be difficult to predict using conventional systems of equations of the Kermack–McKendrick theory. A new method for forming modeling structures with the included logic that sets the conditions for redefining the system of equations has been developed. It has been proposed to identify key events for changing the right-hand sides of the system of equations on the basis of tracking the changing evolutionary characteristics and transforming parameters of the interaction between the aggressive agent and the environment. Continuous evolution causes the wave-like dynamics; therefore, repeated virus activity outbreaks have been observed. To model the evolving biophysical processes, several wave equations at once should be used, since the properties of oscillations are not preserved. A hybrid model of wave differential equations has been built from a set of redefined activation and damping functions of oscillations selected according to specified conditions, while the oscillation minima remain positive and the wave maxima do not increase indefinitely. Using a new original method, consequences of the event-driven pathogen evolution has been simulated, which is especially reflected on the characteristics of a new series of COVID wave oscillations. Based on the algorithmic implementation of the structure of transitions between behavioral modes in a series of simulation scenarios for the development of epidemic waves in regions depending on immunization factors and estimated efficiency of anti-epidemic measures, scenarios for the development of the epidemic situation with a change in the dominant strains of coronavirus in five regions have been obtained. The method for organizing hybrid models from variable sets of wave equation forms can be applied to the scenario modeling of many stage oscillatory transient modes that arise both during the formation of new neural connections and in electrical circuits with feedback and trigger switching. The physical, biophysical, and social wave processes have a surprisingly large number of common dynamic aspects. Pulse and rapidly damping phenomena similar to epidemic waves are observed, for example, when waves of negative reactions spread in indignant social networks to information with the deliberate dissemination of shocking content. In social networks, there are groups that actively spread the impact and slow down this indignation, as in physics. The main problem in 2005 is the activity of the group of chronic “Long COVID” spreaders.

【Objective】Accurate estimation of reference crop evapotranspiration (ET0) is essential for determining crop water requirements, improving irrigation efficiency and supporting sustainable water resource management, especially in regions facing water scarcity. The objective of this paper is to identify a reliable and practical model for estimating ET0 in Northern Henan Province.【Method】Daily meteorological data measured from 2021 to 2022 and numerical weather forecasts from 2023 for Xinxiang City, Henan Province, were used to develop and evaluate the following ET0 models: the Prophet model, the autoregressive integrated moving average model (ARIMA), the extreme learning machine (ELM) model, and their hybrid combinations. ET0 calculated using these models were compared with that calculated using the FAO-56 Penman-Monteith method.【Result】ET0 calculated in all models were correlated with maximum temperature, minimum temperature, solar radiation, and wind speed 2 m above the ground surface. They factors were thus selected as inputs to the models. The time-series models (Prophet and ARIMA) effectively captured seasonal variation in ET0 but gave rise to notable errors when ET0 exceeded 5.5 mm/d. The ELM model better captured the nonlinear relationship between ET0 and these meteorological factors, achieving an increase of R2 value by 11%, compared with the time-series models. The ELM-ARIMA hybrid model was more accurate than other models for calculating ET0 in medium-term (1-10 day), with its MAE, RMSE and MBE reduced by 64.5%, 72.9% and 65.6%, respectively, compared to those in the non-hybrid model; its correlation with observed ET0 was R2=0.945, the highest among all models.【Conclusion】The ELM-ARIMA hybrid model is most accurate and reliable for calculating ET0 and is recommended for use in water resource management and agricultural planning in Northern Henan Province.

Accurate simulation of atmospheric photochemistry is essential for air quality and climate studies but computationally expensive in three‐dimensional atmospheric models. Artificial intelligence (AI) algorithms show promise for accelerating photochemical simulations, but integrating them reliably into numerical models as replacements for complex mechanisms has been challenging, with success mostly limited to simplified schemes (e.g., 12 species). We present a novel AI PhotoChemistry (AIPC) scheme using the Feature‐Mapping Subspace Self‐Attention (FMSSA) algorithm, enabling fast, accurate, and stable online simulation of the full SAPRC‐99 mechanism (79 species, 229 reactions) within WRF‐Chem. Feature‐mapping subspace self‐attention reduces computational cost by 91% versus standard attention architectures via global feature mapping and subspace attention decomposition while maintaining high fidelity to nonlinear chemistry. Offline evaluations show FMSSA's superior accuracy (mean NRMSE = 3.09% for 69 species) over Multi‐Layer Perceptron and Residual Neural Network baselines, especially for ozone. Ablation experiments confirm the critical role of attention and LayerNorm modules for accuracy and generalizability. Monthly‐scale online simulations conducted in August show stable FMSSA‐AIPC performance, accurately reproducing species spatiotemporal distributions with 77% faster computation than the numerical solver. However, simulations conducted in February show performance degradation for all AIPC schemes, with FMSSA‐AIPC exhibiting unique synchronous errors, highlighting generalization challenges across significantly distinct atmospheric regimes. This work advances integrating sophisticated chemical processes in weather and climate models, with future efforts targeting expanded training data sets, architectural refinements and broader spatiotemporal testing. Plain Language Summary Atmospheric photochemistry critically influences air quality and climate change by modulating atmospheric composition, but simulating these processes within three‐dimensional atmospheric models is computationally expensive, particular for sophisticated mechanisms, hindering high‐resolution studies and integration into Earth system models. While artificial intelligence (AI) algorithms demonstrate potential for accelerating photochemical simulations, the highly nonlinear reaction networks of sophisticated mechanisms restrict the reliable integration of AI PhotoChemistry (AIPC) schemes into numerical models, with successful implementations predominantly limited to oversimplified mechanisms (e.g., 12 species). Here, we developed a novel AIPC scheme using the feature‐mapping subspace self‐attention (FMSSA) algorithm, which enables fast, accurate, and stable monthly‐scale online continuous simulations of the entire SAPRC‐99 mechanism (79 species, 229 reactions) within WRF‐Chem. FMSSA reduces computational time by 77% compared to traditional solvers and outperforms multi‐layer perceptron and residual neural network baselines, particularly for ozone. However, FMSSA exhibits unique synchronization errors during online continuous simulations when atmospheric conditions significantly differ from those in the training phase. This work advances the integration of complex photochemical mechanisms into weather and climate models, but future efforts are needed to extend FMSSA to more mechanisms and improve its stability across broader spatiotemporal conditions. Key Points Feature‐mapping subspace self‐attention (FMSSA) surpasses multi‐layer perceptron and residual neural network in modeling photochemistry The FMSSA‐based scheme enables accurate and stable simulations of full SAPRC‐99 photochemical mechanism within WRF‐Chem The FMSSA‐based scheme reduces computation time by 77% versus the SAPRC‐99 numerical scheme