Stochastic cloning of dynamical systems with hidden variables

We present an approach combining reservoir computing and nonlinear dynamics to replicate the behavior of stochastic systems, even when only partial observations are available. Unlike conventional RC applications, our approach systematically evaluates the conditions under which a system can be "strongly" cloned (exact trajectory prediction) versus "weakly" cloned (statistical replication), leveraging external noise excitation to infer hidden dynamics. By applying external noise and analyzing the system response, we demonstrate the feasibility of our approach both theoretically and experimentally. We show that strong cloning is achievable only when a deterministic functional relationship exists between the external noise and the system's response. Using the FitzHugh-Nagumo neuron model and a diode-pumped erbium-doped fiber laser as test cases, we show that a "strong" clone-capable of accurately predicting system dynamics-can be constructed for the neuron model, whereas only a "weak" clone, capable of statistical prediction, is achievable for the laser system. These findings underscore the potential of leveraging machine learning and nonlinear dynamics for system identification and prediction in complex real-world scenarios.