Weather Forecasting Based on Data-Driven and Physics Informed Reservoir Computing Models

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Due to the continued increase of energy demand, conventional energy sources seem unable to support energy 36 advances in recent years. Global energy consumption is predicted to be grown by around 60% by 2030 (Bahrami     disadvantage is a single model to learn entire wind speed conditions. Therefore, recent studies employ hybrid 72 models that combine several approaches to reach more accurate results (Wang et al., 2019). (Hu et al., 2021) 73 suggests three models' structure namely, (I) decomposition by employing variational mode decomposition, (II) 74 optimization by using differential evolution, and (III) forecasting the assembly of decomposed variables in the

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One unique approach was presented by (Zhang and Pan, 2020), author uses a hybrid approach by incorporating 81 Elman-radial Basis function and Lorenz disturbance to acquire more accurate results. Their study employs wavelet 82 transform (WT) and ESN with ensemble techniques.

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In addition, AI techniques have a promising advantage over physical and statistical models, however, there is a 84 drawback of robust in reliability for scientific applications and decision-making processes. The main obstacle 85 highlighted in (Kashinath et al., 2021), is that the model's deficiency in observing the physical phenomena of the 86 system. (Tian, 2020) stated that scholars analysing wind speed rarely consider its chaotic nature, where the system 87 has strong nonlinearity and uncertainty. There is an interesting contribution made to resolve this issue in (Zhang   Recognizing the challenges of single models, this paper proposes a hybrid wind speed forecasting approach by 99 simultaneous assessment of two modules. Initially, the wind speed forecasting module was evaluated in three 100 steps: decomposition, optimization, forecasting. First, in the decomposition module, the WT is used to eliminate 101 the noise of original wind speed data and decompose it into several sub-signals with better counters and behaviour.

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Second, reservoir computing is utilized for all decomposed sub-series. Third, RNN is optimized with RMSprop 103 (Keras) to obtain better results. Then, the dynamic behaviour of atmospheric conditions is simulated by the Lorenz 104 system. First, the chaotic behaviour of atmospheric changes in pressure and temperature is defined by Lorenz 105 equations and incorporated into PIML. Second, physics informed ESN algorithm is employed due to its advantage 106 in describing the chaotic dynamics over traditional reservoir computing methods. Third, the study utilizes chaotic

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Recycle validation for robust and performance of validation strategy; and Bayesian optimization to compute 108 optimal hyperparameters that are suggested in (Racca and Magri, 2021). Finally, the feasibility and reliability of

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Following their finding, this study contributes to the renewable energy development of Gazanjyk by proposing a 113 wind forecasting method to secure the stable and reliable performance of wind energy and promote the safety of 114 the power system.

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The rest of this article is organized as follows: Section 2 introduces reservoir computing and the structure of PIML.

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Section 3 shows the implementation steps of the data-driven method. Section 4 describes the effectiveness of

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The weather prediction process of the proposed framework is shown in Figure 1. The process contains two stages: 126 the wind speed and atmospheric system models. The details of the framework are explained as follows:

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Stage 1: the original data on wind speed performance is collected. Then, the decomposition of time-series data is 128 performed by WT. In this step, the wind speed data is separated into approximate sub-signal and the respective 129 detail sub-signals. After, the time-series data is split into training sets for the training model and test sets for 130 validation purposes. Consequently, the reservoir computing approach or RNN is used to construct a wind speed 131 forecasting model.

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Stage 2: the Lorenz system is employed to describe the chaotic state of the atmospheric system. The physics-133 informed reservoir computing is utilized to time-accurately forecast the system. In particular, the ESN is

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In other words, ANN is based on nodes connected between layers and limited to links within a hidden layer.

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Whereas in RNN this connection is provided, therefore the output has access to the input of the current hidden 162 layer as well as to the output of the previous one. That enables effective learning of time-series data and makes it 163 consistent with wind speed forecasting. Figure 2 illustrates the architecture of RNN.

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The linear combination of input and reservoir state makes RC the best alternative for nonlinear system forecasting 175 of dynamical systems. This approach is also known as echo state networks (ESN).

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This helps to understand original wind speed performance through low-frequency approximate sub-signal and 263 several high-frequency detail sub-signals. Figure 5 presents the results of WT that serve as a basis for sequent 264 steps in the wind speed forecasting model.  helps to ignore initial steps to minimize the noise that may mislead the model. Figure 6 illustrates that the model 291 has learned daily oscillations of wind speed. However, it frequently misrepresents the peaks of the original 292 distribution. Therefore, the model is capable to mimic the wind speed swings in general, however, limited to 293 match the unexpected peaks. In conclusion, the model is limited for accuracy given the wind speed input signals.

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The first aspect is the long computation time. Even with a defined early stop for optimal loss in 20 epochs with 309 100 sub-epochs in each time-step, the proposed model has ended with a wall time of 26 min and 51 sec. Second, 310 you cannot get convergence proof. The third aspect is the requirement for a large dataset.

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One approach to overcome the previously stated shortcoming of the data-driven wind speed forecasting model is

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The reconstruction of the next objective function is achieved by the mean and standard deviation of GP, which 372 was used to optimize the acquisition function of the following point in the enlarged dataset. This study employed 373 a scikit-optimize Python library with BO based on 5 × 5 starting points and GP regression computed 24 points.

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The performance of PI-ESN was computed by MSE for both validation and test datasets. The results of the chaotic 375 system could be observed in GP process reconstruction. Figure 8

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In summary, the novel PI-ESN model overcomes the previously stated challenges of conventional PIML 400 approaches. The proposed hybrid method demonstrates accurate performance and robustness for chaotic system 401 forecasting that outperform conventional stand-alone wind speed prediction models such as physical, statistical 402 and machine learning algorithms.

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Considering increasing global energy consumption and the anticipated rise of energy demand, there is a need for 405 renewable energy sources to support sustainable advancement in major energy suppliers. Wind power is 406 considered an environmentally sustainable source of renewable energy with less significant attention given to its 407 utilization. The study focuses on wind power due to the potential of solar and wind power sources that is 408 overshadowed by the exploitation of oil and gas resources in Turkmenistan, which is the major energy supplier in