Quantum Mechanics for Stochastic Closure of Dynamical Systems

We present a framework for stochastic closure of dynamical systems that models the unresolved degrees of freedom as a quantum mechanical system. Given a system in which some component of the state is unknown, this method involves defining the system as being in a time-dependent "quantum-state" which influences the tendency of a random draw of the unknown components of the state vector. This quantum state evolves under the action of a Koopman operator, and is updated at each timestep of the coarse-grained model according to a quantum Bayes' rule. We demonstrate the consistency of this scheme in reproducing the statistical behavior of the original system with applications to the Lorenz 63 and two-level Lorenz 96 systems.