High Dimensional Hybrid Reservoir Computing

Kurzfassung

Reservoir Computing (RC) is getting popularity as an alternative solution for complex dynamical systems, where physically derived models reach their limitation. RC is by default fully data-driven method and is expected to learn the underlying system in the dataset. However RC can't do so for a lack of data quantity, for example. The hybrid approach is now recognized as a powerful option for it. The idea is to combine a knowledge-based model as a support (e.g. an imperfect governing equation) to the fully data-driven method. This combination can be done at the input, output layer of RC or both of them (respectively called, input-, output-, full-hybrid). Some studies have been already done, for example, input- and full-hybrid by Pathak et al.(2018), output-hybrid by Doan et al.(2019). Duncan et al.(2023) compared the performance of the three approaches and showed the superiority of output-hybrid compared to the others. The prior studies above have developed the hybrid approach in lower dimensional problems (e.g. three dimension). In this work, we will extend the hybrid approach to higher dimensional systems. This will allow to treat highly nonlinear and time evolutionary systems with system knowledge, such as fluid dynamics simulations and time evolutionary phenomena captured in two-dimensional images.