2025/05/12 by Vales, Chris, Freeman, David C., Slawinska, Joanna +1 · 1 citation
#Computational Physics (physics.comp-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences
paper · doi:10.48550/arxiv.2505.07519
We develop a framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into an infinite dimensional quantum mechanical system, we use the space of quantum states to model the unresolved degrees of freedom of the original dynamics and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is projected to finite dimension by a positivity preserving discretization process. Based on methods from operator valued kernels and delay embedding, the compressed finite dimensional representation of the dynamics is invariant under the spatial symmetries of the original dynamics. We develop a data driven formulation of the scheme that can be realized numerically and apply it to a dynamical closure problem for the shallow water equations. The results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.