This paper explores the prediction of the dynamics of piecewise smooth maps
using various deep learning models. We have shown various novel ways of
predicting the dynamics of piecewise smooth maps using deep learning models.
Moreover, we have used machine learning models such as Decision Tree
Classifier, Logistic Regression, K-Nearest Neighbor, Random Forest, and Support
Vector Machine for predicting the border collision bifurcation in the 1D normal
form map and the 1D tent map. Further, we classified the regular and chaotic
behaviour of the 1D tent map and the 2D Lozi map using deep learning models
like Convolutional Neural Network (CNN), ResNet50, and ConvLSTM via cobweb
diagram and phase portraits. We also classified the chaotic and hyperchaotic
behaviour of the 3D piecewise smooth map using deep learning models such as the
Feed Forward Neural Network (FNN), Long Short-Term Memory (LSTM), and Recurrent
Neural Network (RNN). Finally, deep learning models such as Long Short-Term
Memory (LSTM) and Recurrent Neural Network (RNN) are used for reconstructing
the two parametric charts of 2D border collision bifurcation normal form map.

本研究探讨了使用各种深度学习模型来预测分段平滑映射的动力学。通过使用深度学习模型，我们展示了预测分段平滑映射动力学的各种新颖方法。我们还使用机器学习模型如决策树分类器、逻辑回归、K 近邻、随机森林以及支持向量机来预测一维正规形式映射和一维帐篷映射中的边界碰撞分叉。此外，我们通过混沌图和相图，使用卷积神经网络（CNN）、ResNet50 和 ConvLSTM 来对一维帐篷映射和二维 Lozi 映射的规则和混沌行为进行分类。我们还使用前馈神经网络（FNN）、长短期记忆（LSTM）和循环神经网络（RNN）等深度学习模型来对三维分段平滑映射的混沌和超混沌行为进行分类。最后，我们使用长短期记忆（LSTM）和循环神经网络（RNN）来重建二维边界碰撞分叉正规形式映射的两个参数图。