Learning Latent Space Dynamics with Model-Form Uncertainties: A Stochastic Reduced-Order Modeling Approach
This work addresses uncertainties in reduced-order modeling for complex systems like fluid mechanics, but it is incremental as it builds on existing literature by combining known techniques.
The paper tackles the problem of representing and quantifying model-form uncertainties in reduced-order modeling of complex systems, such as fluid mechanics, by proposing a probabilistic approach that uses operator inference and randomization of the projection matrix, with efficacy assessed on canonical problems to identify and quantify uncertainties.
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an appropriate state-space representation, in the projection step that underlies many reduced-order modeling methods, or as a byproduct of considerations made during training, to name a few. Following previous works in the literature, 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 - acting on a subset of the Stiefel manifold - 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.