This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

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使用算子推理从数据中学习非线性简化模型

本综述讨论了算子推理，这是一种非侵入式简化建模方法，该方法通过为简化模型定义结构化多项式形式来合并物理控制方程，然后从模拟训练数据中学习相应的简化算子。算子推理的多项式模型形式具有足够的表现力，可以涵盖流体力学和其他科学与工程领域中发现的广泛非线性动力学，同时仍然提供高效的简化模型计算。算子推理的学习步骤植根于经典的基于投影的模型简化；因此，一些丰富的模型简化理论可以应用于通过算子推理学习的模型。这种与基于投影的模型简化理论的联系提供了一条导出误差估计和获得见解以改进预测的途径。此外，通过保留哈密顿量和其他结构的算子推理公式，可以在超出训练范围的简化模型的预测中保证能量守恒等重要物理属性。本综述通过大规模燃烧示例说明了算子推理的关键计算步骤。