# Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review
## 3 Neural Network-Based Forecasting Approaches
### ANN-Based Forecasting Approaches  
ANN has multiple perceptrons' or nodes at each layer. For example, the network with two input nodes, two hidden layers with four nodes in each, and one output node is shown in Figure 4. This network can be called FFNN when its inputs are processed forward (refer to the red dotted line in Figure 4). The FFNN is one of the most straightforward neural networks, and it passes information in one direction through various input nodes until the output node [178]. This type of neural network may or may not have hidden layers, making its functioning more understandable. Some advantages of FFNN include storing information on the entire network, working with incomplete knowledge, offering tolerance, and having distributed memory. However, the disadvantages of FFNN include having hardware dependency and unexplained behavior that can leave us tormented with results. No particular rule for deciding the network's structure and the appropriate network structure is achieved through experience and trial and error. BPNN is an essential mathematical tool for improving the accuracy of predictions in data mining and machine learning. In FFNN, the network propagates forward to obtain the output and compares it with real value to obtain the error. However, to minimize the error, the BPNN will propagate backward by finding the error derivative for each weight and then subtracting this value from the weight value. The architecture of a BPNN is also shown in Figure 4, and the direction of propagation is shown in the green dotted line. On the other hand, RNN is more complex than FFNN and BPNN. Here, the RNN's every node acts as a memory cell and continues the operations computation [4]. The RNN saves the output of processing nodes and feeds them back into the network, and hence, they do not pass the information in one direction only (refer to the blue dotted line in Figure 4). If the network's prediction is incorrect, the system self-learns and continually works toward correcting the forecast during backpropagation. Researchers have utilized ANNs in numerous applications to predict or forecast various chaotic systems' behavior. For instance, in [25], the researchers developed the  
Figure 3: Summary of multiple techniques developed using ANN, FNN, WNN, and optimization-based approaches for chaotic time series forecasting. complex weighted neural network method for high-resolution adaptive bearing prediction. It is observed that this concept is especially effective in circumstances where the hermit matrix progressively changes over time due to adaptive tracking. [PERSON] et al. proposed the application of ANN in power systems for predicting the one-day-ahead daily peak load based on chaotic time series data using absolute error as a performance measure [26]. It is to be noted that the proposed technique can also be used for other forecasting applications, such as predicting the special days, hourly load, temperature, etc. In [27], the researchers have presented the RNN model for Mackey-Glass chaotic time series. The proposed model's experimental results are more practicable and effective in making short-term predictions for chaotic time series than the multi-dimension embedding phase space method. [PERSON] et al. developed a multilayer neural network adaptive control algorithm for disturbance compensation in nonlinear systems. The work remarks that this developed algorithm can also be used simultaneously for nonlinear systems with mismatched uncertainties. Additionally, an extended state observer was employed to estimate the exogenous disturbance and predict the system's state [179]. In extension, the authors presented the integration of a full-state feedback control algorithm, adaptive neural network, and extended state observer to handle the unknown nonlinear dynamics and external disturbances.