# Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review
## 3 Neural Network-Based Forecasting Approaches
### ANN-Based Forecasting Approaches
An expectation-maximization parameter learning algorithm for the developed model was used for probability threshold prediction during the out-of-sample validation. The experimental result from the system proves the viability of the proposed technique and shows better results than the ANN model alone. In [68], the work presented the RBFNN model to predict the Shanghai Composite index that is chaotic according to the phase diagram analysis. The proposed technique's experimental results are better than the BPNN. In [78], the hybrid Elman-NARX neural network model is presented to chaotic systems, such as Mackey-Glass, Lorenz equations, and the real-life sunspot time series, for predicting the chaotic time series. The proposed method has performed more effectively and accurately than the AR model, GA, and fuzzy methods. [PERSON] et al. presented the rough set neural network model for long-term wind power prediction [80]. The experimental results show that the rough set method has the least NMAE compared to the other three methods, the chaos neural network model, persistence model, and rough set neural network model. Another forecasting method for gas emission rate prediction, known as the global method based on the BPNN, was proposed in [83]. The proposed model showed good accuracy and stability predictions than the first-order weighted local prediction method. In [84], the researchers developed the chaotic RBFNN method for predicting the power systems' short-term load. The results of the proposed method showed promising results better than conventional RBFNN. In [12], a chaos RBFNN method was presented for forecasting the gasoline engine intake flow's transient condition. The simulation results showed more accuracy compared to conventional RBFNN. In [101], the application of ANN in a chaotic dynamical system for forecasting embedded dimension and robust location was presented. In [103], the selecting and combining models with the SOM neural network model for long-term chaotic time series prediction from the Mackey-Glass equation, NN5 tournament, AR model, and sine function were presented. It is to be noted that this model can be used to assess the selected outcomes of the modeling techniques by considering the best-predicted SMAPE. In [21], the MLP model for enhancing the accuracy of a flood prediction through machine learning and chaos theory was presented. The experimental results of the proposed method performed better than the Elman-RNN method. It is to be noted that this concept is also applicable to sensors, allowing for more individual action in severe conditions. Further, the idea can also lower the system's total operational costs and ensure next-generation power grids' effective and reliable functioning. In [182], the authors developed a hybrid machine learning technique for forecasting the time series of NN5 using the nearest trajectory model, one-year-cycle model, and neural network. In [128], the self-adaptive chaotic BPNN algorithm was proposed based on Chebyshev's chaotic map for predicting the electrical power system's load. The presented algorithm results showed better global optimization performance than conventional BPNN, RBFNN, and Elman networks. The work highlights that the chaotic neural network regression using the probability density forecast method can predict the electricity demand. In [131], the deep CNN model was proposed for forecasting Lyapunov exponents from observed time series in discrete dynamical systems. In [157], the authors presented the RNN-based LSTM model to predict the mutation rate in a human body affected by COVID-19. The proposed approach can be extended further by inserting and deleting mutation rates in the model. The authors of [162] presented the Deep CNN model using meteorological data to forecast flight delays. The results of Deep CNN showed to be better than the CNN, which is proven in terms of weight gradient error and hidden layer error.