Dynamic Modelling from data is of great significance for understanding the evolution of complex systems. In this work, inspired by manifold learning framework of Charts and Atlases for Nonlinear Data-Driven Dynamics on Manifolds (CANDyMan), we propose the Density-based Decomposition on Manifold with Autoencoder Reduction (DDMAR) method, for discovering the intrinsic coordinates and for reconstructing complex dynamical behaviours with multiple outliers.
Firstly, the density-based spatial clustering is employed to decompose the manifold structure into atlases, subsequently setting overlapping regions for adjacent atlases to achieve dynamic evolution. Then, an automated selection method of clustering parameters, which is different from prior settings, is developed for structural decomposition. On this basis, the reconstruction is accomplished by an autoencoder to reduce dimensionality, combined with feedforward neural network to achieve learning of low-dimensional dynamic behaviours. The results demonstrate that, DDMAR method is capable of automatically setting parameters based on the core point principle, making the manifold learning of dynamics more reliable and stable. Moreover, it exhibits good robustness to outliers, thereby enabling the extraction of intrinsic coordinates and the reduction of reconstruction errors. Additionally, it produces smoother dynamics in the reconstructed transition region. This work promotes the development of dimensionality reduction and reconstruction methods for complex manifolds with outliers in high-dimensional dynamical systems.