Conditional Gaussian Framework with Stochastic Data-Driven Multiscale Reduced Order ROMs
REFERENCE: Mou, C., Chen, N., & Iliescu, T. (2023). An Efficient Data-Driven Multiscale Stochastic Reduced Order Modeling Framework for Complex Systems. Journal of Computational Physics, 112450. Β
Figure. A flowchart of the conditional Gaussian framework.
A natural way to build stochastic closure ROMs with a reduced dimension of the coupled system of the state variable u is to project it onto its large- and medium-scale components v and w
One desirable feature of the ROM framework above is that the conditional mean and the conditional covariance can be solved via the following closed analytic formulae: