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.

翻译：本文提出了一种概率方法，用于在使用算子推断技术对复杂系统进行降阶建模时表示和量化模型形式不确定性。此类不确定性可能源于适当状态空间表示的选择、许多降阶建模方法基础的投影步骤，或是训练过程中所做考虑的副产品等。遵循文献中的先前工作，所提出的方法通过随机化投影矩阵来扩展近似空间，从而捕捉这些不确定性。这是通过将作用于Stiefel流形子集上的黎曼投影和收缩算子与信息论公式相结合来实现的。该方法的有效性通过在流体力学经典问题上识别和量化模型形式不确定性对推断算子的影响来评估。