Data driven modeling of self-similar dynamics

Complex systems modeling is essential for understanding, predicting, and even controlling a complex system. Due to the non-linear, self-organizing, emergence, and other complex behaviors in them, modeling complex systems has always been challenging. In recent decades, data-driven approaches, leading by machine learning, have shown significant advantages in so many fields, which inspired us to do better in modeling complex systems. On the other hand, self-similarity is a common feature of complex systems. From natural systems, like the fractal structure of vegetation clusters in the Amazon rainforest and the Tibetan plateau[1], the critical phenomena in atmospheric precipitation[2], to societal systems like network traffic[3], the avalanche of public opinion in social medias[4], and neural system like critical phenomenon in brain[5, 6, 7, 8] and so on, there are so many evidences of scale-invariant properties in complex systems. Thus, we're motivated to integrate self-similarity as prior knowledge, aiming for data-driven multi-scale modeling of complex systems. Two aspects of modeling complex systems are network structure and dynamics.