Mixed interpolatory and inference non-intrusive reduced order modeling with application to pollutants dispersion

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.