Reduced-order models (ROMs) capture the key physical mechanisms of full-order models but with fewer degrees of freedom. A first step in reduced-order modeling is dimensionality reduction, which involves modeling high-dimensional data in a lower-dimensional space (manifold). A second step of reduced-order modeling is to model the temporal dynamics on the manifolds. This can be achieved via projection-based methods (Galerkin projection), which project the dynamics onto the reduced space, or via machine learning approaches such as ESNs and Long Short-Term Memory networks (LSTMs), which learn the temporal evolution directly from data. Both approaches, however, are global methods, i.e., they are optimized over the entire dataset. In this work, we develop local reduced-order models by seamlessly combining linear autoencoding and cluster-based analysis. By creating a cartography of the manifold and capturing the dynamics within local patches centered at the centroids found by clustering, we obtain an accurate representation of the system’s dynamics. Our methodology is verified on a prototypical chaotic model, the Rössler attractor, and then applied to the Kuramoto-Sivashinsky equations in both bursting and chaotic regimes. Our findings demonstrate the potential of local approaches in predicting nonlinear dynamics with reduced computational cost, opening opportunities for efficient flow control and real-time prediction in engineering applications.