Modelling complex dynamical systems in a data-driven manner is challenging due to the presence of emergent behaviors and properties that cannot be directly captured by micro-level observational data. Therefore, it is crucial to develop a model that can effectively capture emergent dynamics at the macro-level and quantify emergence based on the available data. Drawing inspiration from the theory of causal emergence, this paper introduces a machine learning framework aimed at learning macro-dynamics within an emergent latent space. The framework achieves this by maximizing the effective information (EI) to obtain a macro-dynamics model with stronger causal effects. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed framework. Not only does it successfully capture emergent patterns, but it also learns the coarse-graining strategy and quantifies the degree of causal emergence in the data. Furthermore, experiments conducted on environments different from the training dataset highlight the superior generalization ability of our model.

通过最大化有效信息来学习宏观动力学模型，进而捕捉和量化数据中的因果性出现模式，并展示了模型在模拟和真实数据上的有效性和优良的泛化能力。

数据中的发现：启发式学习因果涌现