通过分层结构提升降阶模型学习效率，误差更低且可动态更新。
Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Models
- 基于降维空间的层级结构，迭代优化初始猜测值。
- 在相同离线时间下，误差比传统方法低4倍。
- 适合需要动态更新基底或模型形式的复杂系统建模。
本文提出一种数据驱动的嵌套算子推断（Nested Operator Inference, OpInf）方法，用于从高维动力系统快照数据中学习物理信息引导的降阶模型（ROM）。该方法利用降维空间内的固有层次结构，迭代构建OpInf学习问题的初始猜测，优先考虑主导模态间的相互作用。对于任意目标降维维度，所计算的初始猜测对应的ROM在快照重构误差上严格小于或等于标准OpInf。此外，该嵌套OpInf算法可从先前学习的模型进行热启动，支持基底和模型形式动态更新的多样化应用场景。我们在一个三次热传导问题上验证了该算法性能：在相近离线时间下，嵌套OpInf的误差为标准OpInf的1/4。进一步应用于格陵兰冰盖的大规模参数化模型，尽管存在模型形式近似误差，仍能学习到平均误差3%、计算加速超过19,000倍的降阶模型。
原文摘要 · Abstract (English)
This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy within the reduced space to iteratively construct initial guesses for the OpInf learning problem that prioritize the interactions of the dominant modes. The initial guess computed for any target reduced dimension corresponds to a ROM with provably smaller or equal snapshot reconstruction error than with standard OpInf. Moreover, our nested OpInf algorithm can be warm-started from previously learned models, enabling versatile application scenarios involving dynamic basis and model form updates. We demonstrate the performance of our algorithm on a cubic heat conduction problem, with nested OpInf achieving a four times smaller error than standard OpInf at a comparable offline time. Further, we apply nested OpInf to a large-scale, parameterized model of the Greenland ice sheet where, despite model form approximation errors, it learns a ROM with, on average, 3% error and computational speed-up factor above 19,000.
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