Inferring the dynamics of black-box systems using a learning machine

Given a segment of a time series of a system at a particular set of parameter values, is it possible to infer the dynamic behavior of the system in its parameter space? Here, we show that this goal can be achieved to a certain extent using a self-evolution learning machine. It is found that following an appropriate training strategy that monotonously decreases the cost function, the learning machine in different training stages is just like the system at different parameter sets. Consequently, the dynamic properties of the system are, in turn, usually revealed in the simple-to-complex order. The underlying mechanism can be attributed to the training strategy, which results in the learning machine collapsing to a qualitatively equivalent system of the system behind the time series. Thus, the learning machine enables a novel way of probing the dynamic properties of a black-box system without artificially establishing the equations of motion. The given illustrative examples include a representative model of low-dimensional nonlinear dynamical systems and a spatiotemporal model of reaction-diffusion systems.

Automated summary

The study shows that by using a self-evolution learning machine with a training strategy that gradually decreases the cost function, it is possible to infer the dynamic behavior of a system and gradually reveal its dynamic properties during training.