Parameter Estimation of Lorenz Attractor: A Combined Deep Neural Network and K-Means Clustering Approach

This research is mainly aimed at introducing a deep learning approach to solve chaotic system parameter estimates like the Lorenz system. The reason for the study is that because of its dynamic instability, the parameter of the chaotic system cannot be easily estimated. Moreover, due to the complexity of chaotic systems based on existing approaches, some parameters may be difficult to determine in advance. Therefore, it is crucial to assess the parameter of chaotic systems. To solve the issue of parameter estimation for a chaotic system, deep learning is utilized. After that, it has been suggested to improve the efficiencies in the Deep Neural Network (DNN) model by combining the DNN with an unsupervised machine learning algorithm, the K-Means clustering algorithm. This study constructs the flow of DNN based method with the K-Means algorithm. DNN techniques is suitable in solving nonlinear and complex problem. The most popular method to solve parameter estimation problem is using optimization algorithm that easily trap to local minima and poor in exploitation to find the good solutions. Due to the flow, 80% of training and 20% test sets for each class are divided between the Lorenz datasets. Accuracy by using 80:20 ratio of training and test data gives result 98% of accurate training data, and 73% of test data are predicted with the proposed algorithm while 91 and 40% of the DNN models are predicted in training and test data.