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近年来，基于神经网络的机器学习方法取得了突破性进展<ref>Vlachas P-R, Arampatzis G and Uhler C et al. Multiscale simulations of complex systems by learning their effective dynamics. Nat Mach Intell 2022; 4: 359–366.</ref><ref>Kemeth F-P, Bertalan T and Thiem T et al. Learning emergent partial differential equations in a learned emergent space. Nat Commun 2022; 13: 3318.</ref><ref>Floryan D and Graham M-D. Data-driven discovery of intrinsic dynamics. Nat Mach Intell 2022; 4: 1113–1120.</ref><ref>Cai L and Ji S. A multi-scale approach for graph link prediction. Proceedings of the AAAI Conference on Artificial Intelligence, New York, 20-27 February 2020.</ref><ref>Chen Z, Li S and Yang B et al. Multi-scale spatial temporal graph convolutional network for skeleton-based action recognition. Proceedings of the AAAI Conference on Artificial Intelligence, New York, 22 February - 1 March 2022.</ref>，借助此方法，以数据驱动的方式自主发现复杂系统的因果关系、因果机制，以至动力学都成为可能。此外，机器学习和神经网络还可以帮助我们找到更好的粗粒化策略、从数据中发现宏观层面的因果关系。
近年来，基于神经网络的机器学习方法取得了突破性进展<ref>Vlachas P-R, Arampatzis G and Uhler C et al. Multiscale simulations of complex systems by learning their effective dynamics. Nat Mach Intell 2022; 4: 359–366.</ref><ref>Kemeth F-P, Bertalan T and Thiem T et al. Learning emergent partial differential equations in a learned emergent space. Nat Commun 2022; 13: 3318.</ref><ref>Floryan D and Graham M-D. Data-driven discovery of intrinsic dynamics. Nat Mach Intell 2022; 4: 1113–1120.</ref><ref>Cai L and Ji S. A multi-scale approach for graph link prediction. Proceedings of the AAAI Conference on Artificial Intelligence, New York, 20-27 February 2020.</ref><ref>Chen Z, Li S and Yang B et al. Multi-scale spatial temporal graph convolutional network for skeleton-based action recognition. Proceedings of the AAAI Conference on Artificial Intelligence, New York, 22 February - 1 March 2022.</ref>，借助此方法，以数据驱动的方式自主发现复杂系统的因果关系、因果机制，以至动力学都成为可能。此外，机器学习和神经网络还可以帮助我们找到更好的粗粒化策略、从数据中发现宏观层面的因果关系。
下面介绍两种因果涌现的识别方法：①基于信息分解的[[因果涌现]]识别近似方法、②[[NIS|神经信息压缩器]]方法系列（Neural Information Squeezer，简称NIS）。
=== 基于信息分解的因果涌现识别 ===
=== 基于信息分解的因果涌现识别 ===