(1) Quantification of Emergence
Emergence is one of the typical phenomena in complex systems. However, what is emergence, and how to quantify it, are long-standing questions that have not been well resolved. Since 2022, our research group has focused on the theory of causal emergence, attempting to quantify emergence from the perspective of the causal effects in system dynamics. We independently proposed a theory of emergence quantification based on approximate dynamical reversibility and singular value decomposition. We also developed a machine learning framework called NIS+, for automatically discovering emergence from data.
(2) Automated Modeling of Complex Systems
Automatically constructing models of complex systems based on time series data of observable variables, using techniques such as graph neural networks, causal inference, information theory, and deep learning to learn dynamics, predict behaviors, infer hidden network structures, node states, and other unknown information, and even automatically discover macroscopic variables with causal properties.
(3) Scaling Analysis
In urban systems, biological systems, enterprises, and networks, by uncovering scaling laws at the macro-level in data, these laws can characterize the macroscopic universal patterns of complex systems and provide insights into the mechanisms at the microscopic level.
(4) Open Flow Networks
By modeling complex open systems as directed weighted networks and adding two special nodes—source and sink—we can model a class of flow structures with conservation properties. Potential applications include attention flow analysis in online education and learning systems, attention flow analysis in online forums and websites, commodity flow analysis in international trade systems, and energy flow analysis in ecological food webs.
(5) Machine Learning on Complex Networks
Machine learning provides us with new tools to handle and solve inference problems in complex networks, such as complex network classification, network completion, link prediction, etc.
Representative Publications：
(1) Mingzhe Yang, Zhipeng Wang, Kaiwei Liu, Yingqi Rong, Bing Yuan, Jiang Zhang. Finding emergence in data by maximizing effective information. National Science Review, 2024, nwae279
(2) Jiang Zhang, Ruyi Tao, Keng Hou Leong, Mingzhe Yang, Bing Yuan. Dynamical reversibility and a new theory of causal emergence based on SVD. npj Complex 2, 3 (2025)
(3) Zhang zhang, Arsham Ghavasieh, Jiang Zhang, Manlio De Domenico. Coarse-graining network flow through statistical physics and machine learning. Nat Commun 16, 1605 (2025)
(4) Ying Tang, Jing Liu, Jiang Zhang, Pan Zhang. Learning nonequilibrium statistical mechanics and dynamical phase transitions. Nature Communications volume 15, Article number: 1117 (2024)
(5) Ruiqi Li; Lei Dong; Jiang Zhang; Xinran Wang; Wen-xu Wang; Zengru Di; H.Eugene Stanley ; Simple spatial scaling rules behind complex cities, Nature Communications, 2017, 8: 0-1841
Undergraduate courses: Foundation and Application of Matlab, Computer Modeling and
Simulation, Macro Economics
Postgraduate courses: Artificial Intelligence, Systems Science, System Theory Progress