混合插值和推断非侵入降阶模型及其在污染物扩散中的应用
Mixed interpolatory and inference non-intrusive reduced order modeling with application to pollutants dispersion
摘要：
基于从复杂模拟器中采集的输入-输出时域数据，提出了一种构造性的方法来推断降阶线性、双线性或二次时不变动力学模型，再现基本现象。该方法基本上是基于线性动力系统和逼近论。更具体地说，它依次涉及到插值的插值和Loewner框架，已知是非常通用的和可扩展的大规模数据集，以及一个线性最小二乘问题，涉及到原始数据和减少内部变量。关于侵入式方法，不需要关于操作者的先验知识。此外，与传统的非侵入式算子推理方法相比，该方法省去了测量原全阶模型内部变量的需要。因此，它适用于比标准侵入式和非侵入式方法更广泛的应用范围。该理论已成功地应用于一个机场区域污染物扩散的大涡模拟中，该扩散过程涉及多尺度、多物理场的动力学现象。尽管简单的低复杂度模型，所提出的方法显示出令人满意的结果来预测污染物羽流模式，同时显着更快的模拟。
英文摘要：
On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the underlying phenomena. The approach is essentially based on linear dynamical systems and approximation theory. More specifically, it sequentially involves the interpolatory Pencil and Loewner framework, known to be both very versatile and scalable to large-scale data sets, and a linear least square problem involving the raw data and reduced internal variables. With respect to intrusive methods, no prior knowledge on the operator is needed. In addition, compared to the traditional non-intrusive operator inference ones, the proposed approach alleviates the need of measuring the original full-order model internal variables. It is thus applicable to a wider application range than standard intrusive and non-intrusive methods. The rationale is successfully applied on a large eddy simulation of a pollutants dispersion case over an airport area involving multi-scale and multi-physics dynamical phenomena. Despite the simplicity of the resulting low complexity model, the proposed approach shows satisfactory results to predict the pollutants plume pattern while being significantly faster to simulate.
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