Chimeras
摘要
Chimeras are complex spatiotemporal modes that feature chaos within order, i.e., they contain a chaotic part intermingled spatially with an ordered one. They appear in many strongly coupled nonlinear lattice systems usually with long-range interactions and are long lived. It is speculated that the brain of mammals operates in chimera states in several occasions. In this chapter we focus on chimeras in artificial systems such as metamaterials and use machine learning in order to predict their evolution. Since the lattices we focus on are rather complex, a simple data approach is not very successful. In this direction we use, in addition to the machine learning method, certain real time sensors we call “observers.” These sensors provide ground-truth information in certain spatial locations of the lattice at all times—this aspect is very important for the forecast through machine learning. We utilize three machine learning methods, the simpler feed-forward neural network (FNN), the Long Short-Term Memory (LSTM) networks, and the reservoir computing (RC) recurrent neural networks. From the analysis we find that even a small number of observers greatly improve the data-driven model-free long-term forecasting capabilities of all methods.