为复杂系统降阶建模中的模型形式不确定性提供概率化量化方法。
Learning Latent Space Dynamics with Model-Form Uncertainties: A Stochastic Reduced-Order Modeling Approach
- 通过随机化投影矩阵扩展逼近空间，捕捉建模不确定性。
- 在流体力学典型问题上验证，可有效识别并量化不确定性影响。
- 适合关注模型可靠性与不确定性的工程与科学计算研究者。
本文提出一种概率化方法，用于在复杂系统降阶建模中表示和量化模型形式不确定性，该不确定性可能源于状态空间表示的选择、投影步骤（多数降阶方法的基础），或训练过程中的设计考量。受文献启发，所提方法通过随机化投影矩阵来扩展逼近空间。实现方式结合黎曼投影与回缩算子（作用于史蒂费尔流形的子集）及信息论框架。方法在流体力学的经典问题上进行了评估，成功识别并量化了模型形式不确定性对推断算子的影响。
原文摘要 · Abstract (English)
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.
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