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.

中文翻译：

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使用算子推理从数据中学习非线性约简模型


本文讨论了算子推理，这是一种非侵入式约化建模方法，它通过为化简模型定义结构化多项式形式来整合物理控制方程，然后从模拟的训练数据中学习相应的约化算子。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的各种非线性动力学，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归约;因此，一些丰富的模型归约理论可以应用于使用 Operator Inference 学习的模型。这种与基于预测的模型约简理论的联系为推导误差估计和获得见解以改进预测提供了一条途径。此外，通过保留哈密顿量和其他结构的算子推理公式，可以在训练范围之外的简化模型的预测中保证重要的物理属性，例如能量守恒。本文通过一个大规模燃烧示例说明了 Operator Inference 的关键计算步骤。