更新域属性变化下的DMD算子
Updating DMD Operators for Changes in Domain Properties
AI总结：
本文提出了一种无需重新训练即可更新DMD算子以适应域属性变化的方法，通过调整模型内部动态和空间表示，实现快速且准确的替代模型更新。
摘要：
快速且可靠的替代模型对于地质碳封存项目中的优化、控制和不确定性分析至关重要，然而高保真多相模拟器仍然过于昂贵。动态模式分解（DMD）提供了一种有吸引力的数据驱动降维框架，但其算子是针对单组储层属性训练的。当渗透率或井位发生变化时，传统做法是重新生成快照并重新训练替代模型，从而抹去了大部分的速度优势。本文提出了一种轻量级的替代方法，可在不纳入新模拟数据或重新训练的情况下更新现有DMD或DMD-with-control模型。介绍了两种互补的更新策略。对于渗透率在域内均匀变化的情况，所提出的更新调整模型的内部动态和控制响应，以匹配新的流动时间尺度。当渗透率在空间上变化时，该方法修改空间表示，使高渗透区对模型的降维基有更大的影响。数值实验表明，所提出的更新能够恢复三 percent 以内于重新训练的替代模型的污染物迁移和压力上升，但执行速度比完整重新训练快数百倍。这些方法因此能够实现实时优化和快速what-if研究，同时保持碳封存工作流所需物理真实性。
英文摘要：
Fast and reliable surrogate models are critical for optimization, control and uncertainty analysis in geological carbon-storage projects, yet high-fidelity multiphase simulators remain too expensive. Dynamic Mode Decomposition (DMD) offers an attractive data-driven reduction framework, but its operators are trained for a single set of reservoir properties. When permeability or well location changes, conventional practice is to regenerate snapshots and retrain the surrogate, erasing most of the speed advantage. This work presents a lightweight alternative that updates an existing DMD or DMD-with-control model without incorporating new simulation data or retraining. Two complementary update strategies are introduced. For cases where permeability changes uniformly across the domain, the proposed updates adjust the models internal dynamics and control response to match the new flow timescale. When permeability varies in space, the approach modifies the spatial representation so that high-permeability zones are given greater influence on the models reduced basis. Numerical experiments demonstrate that the proposed updates recover plume migration and pressure build-up within three percent of a freshly trained surrogate yet execute hundreds of times faster than full retraining. These methods therefore enable real-time optimization and rapid what-if studies while preserving the physical fidelity demanded by carbon-storage workflows.
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