We have derived a probabilistic approach to represent and quantify model-form uncertainties in operator inference frameworks (here, the OpInf framework proposed by Peherstorfer & Willcox). Such uncertainties can stem from the selection of an appropriate state-space representation, the projection step that underlies many reduced-order modeling methods, or as a byproduct of considerations made during training, to name a few. The proposed method captures these uncertainties by expanding the approximation space through the randomization of the projection matrix. This is achieved by combining Riemannian projection and retraction operators with an information-theoretic formulation. The efficacy of the approach is assessed on canonical problems in fluid mechanics by identifying and quantifying the impact of model-form uncertainties on the inferred operators, as illustrated below for 2D Navier-Stokes equations.
Further details can be found in:
- J. Y. Yong, R. Geelen, and J. Guilleminot, Learning Latent Space Dynamics with Model-Form Uncertainties: A Stochastic Reduced-Order Modeling Approach, arXiv:2409.00220