CMX Lunch Seminar

I present a data driven dynamical closure scheme for problems governed by partial differential equations. The scheme employs the operator theoretic framework of quantum mechanics to embed the original classical dynamics into an infinite dimensional dynamical system, using the space of quantum states to model the unresolved degrees of freedom of the original dynamics and the quantum Bayes rule to predict their contributions to the resolved dynamics. To realize the scheme numerically, the embedded dynamics is projected to finite dimension by a positivity preserving discretization, leading to a finite dimensional representation that is invariant under the dynamical symmetries of the resolved dynamics. I show numerical results of the application of the developed scheme to a closure problem for the shallow water equations, demonstrating the accurate prediction of the resolved dynamics for out of sample initial conditions.