Chaotic time series prediction based on physics-informed neural operator

This paper investigates the prediction of chaotic time series using physics-informed neural operator (PINO) with different driven methods, such as data-driven method, physics-driven method, and hybrid data-physics- driven method. Here, the chaotic time series are generated from two classical time delayed chaotic systems, including Mackey-Glass equation (MG) and Optoelectronic Oscillator (OEO). The simulation results from these two chaotic systems or experimental results from Optoelectronic Oscillator demonstrate that when there is enough data with good quality, it is possible to train the model solely using data-driven method. Conversely, when possessing complete mastery of the physical prior knowledge, it is also available to train the model solely using physics-driven method, indicating there is no need to prepare label datasets as in data-driven method. However, when dataset quality is poor, for example, contaminated by noise, and precise physical prior knowledge is not fully acquired, the hybrid method will have a better performance.