A Novel Data-Driven Physical Iterative Modeling Approach and Its Application in Quantum Instrumentation

This work is the first to solve the data-driven modeling problem for quantum instrumentation and enables the model built is interpretable. First, a data-driven physical iteration (DPI) modeling approach is proposed to solve the modeling problem of a complex physical system with nonlinear characteristics based on the dynamic behavior of a quantum system described by the phenomenological rate equation. Second, the proposed DPI modeling approach incorporates the fast sampling technique, which is proved feasible by the Taylor mean value theorem, to solve the modeling problem of a nonautonomous system. Third, the convergence of the proposed approach is proved by the least squares criterion and the law of large numbers. Finally, the DPI modeling approach is deployed in the optically pumped magnetometer (OPM) and spin-exchange relaxation-free comagnetometer (SERFCM), the physical parameters of the system are estimated while the quantum instrumentation modeling is completed. Numerical simulations and practical experiments support the theoretical results.