Learning Locally Interacting Discrete Dynamical Systems: Towards Data-Efficient and Scalable Prediction

TL;DR

This paper introduces AR-NCA, a neural network model that learns local interaction rules in discrete dynamical systems, demonstrating high data efficiency, robustness, and scalability for predicting complex global behaviors from local interactions.

Contribution

The paper proposes AR-NCA, a novel neural architecture that effectively learns local state transition rules in discrete dynamical systems, improving generalization, data efficiency, and scalability.

Findings

AR-NCA outperforms existing models in generalization across system configurations.

AR-NCA maintains robustness in data-limited and stochastic scenarios.

AR-NCA achieves spatial dimension-independent prediction scalability.

Abstract

Locally interacting dynamical systems, such as epidemic spread, rumor propagation through crowd, and forest fire, exhibit complex global dynamics originated from local, relatively simple, and often stochastic interactions between dynamic elements. Their temporal evolution is often driven by transitions between a finite number of discrete states. Despite significant advancements in predictive modeling through deep learning, such interactions among many elements have rarely explored as a specific domain for predictive modeling. We present Attentive Recurrent Neural Cellular Automata (AR-NCA), to effectively discover unknown local state transition rules by associating the temporal information between neighboring cells in a permutation-invariant manner. AR-NCA exhibits the superior generalizability across various system configurations (i.e., spatial distribution of states), data efficiency and robustness in extremely data-limited scenarios even in the presence of stochastic interactions, and scalability through spatial dimension-independent prediction.