Structured Latent Space for Lightweight Prediction in Locally Interacting Discrete Dynamical Systems

Modeling the large-scale dynamical systems is a computationally expensive task. This is particularly a problem when the focus is solely on understanding the local behavior or state of the systems. Our primary objective is to determine when the propagation of such local interactions will reach a specific region of interest. Although conventional approaches that reconstruct the states of entire dynamic nodes can be used, they may entail unnecessary computational costs. In this paper, we investigate a Structured Latent space for Localized Prediction (SLLP) for the computationally efficient prediction of local behavior in the dynamical systems. The proposed model comprises a CNN encoder to represent the system in a low-dimensional vector, a LSTM module to learn the dynamics in the vector space, and a MLP decoder to predict the future state of a dynamic node. We evaluate the proposed method in the forest fire and stock market models in the task of predicting the burned state of a tree node and buy state of a investor node in future. We compare the proposed model with general ConvLSTM that reconstructs and predicts the entire systems. The proposed model exhibits similar or slightly worse AUC but significantly reduces computational costs, such as FLOPs (×131) and latency (×4.9), than ConvLSTM when predicting a single dynamic node.