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.

中文翻译：

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利用模型形式不确定性学习潜在空间动力学：一种随机降阶建模方法


本文提出了一种概率方法，使用算子推理技术在复杂系统的降阶建模中表示和量化模型形式的不确定性。这种不确定性可能出现在选择合适的状态-空间表示形式时，出现在许多降阶建模方法的投影步骤中，或者作为训练期间考虑的副产品，仅举几例。根据以前的文献工作，所提出的方法通过投影矩阵的随机化来扩大近似空间，从而捕捉到这些不确定性。这是通过将黎曼投影和缩回算子（作用于 Stiefel 流形的一个子集）与信息论公式相结合来实现的。通过识别和量化模型形式不确定性对推断算子的影响，评估该方法对流体力学中典型问题的有效性。