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.

翻译：局部交互动力系统（如疫情传播、谣言在人群中的扩散及森林火灾）展现出由局部、相对简单且常为随机性的动态元素间相互作用所引发的复杂全局动力学行为。其时间演化通常由有限离散状态间的转移驱动。尽管深度学习在预测建模领域取得了显著进展，但多元素间的此类交互作为预测建模的特有领域尚未得到充分探索。我们提出注意力循环神经细胞自动机（AR-NCA），通过以排列不变方式关联相邻细胞间的时间信息，有效发现未知的局部状态转移规则。AR-NCA在不同系统配置（即状态的空间分布）下展现出卓越的泛化能力、数据效率及在极端数据稀缺场景（甚至存在随机交互时）的鲁棒性，并通过空间维度无关的预测实现可扩展性。