Surrogate modeling for large-scale black-box systems

Abstract

This research introduces a systematic method to reduce the complexity of large-scale blackbox systems for which the governing equations are unavailable. For such systems, surrogate models are critical for many applications, such as Monte Carlo simulations; however, existing surrogate modeling methods often are not applicable, particularly when the dimension of the input space is very high. In this research, we develop a systematic approach to represent the high-dimensional input space of a large-scale system by a smaller set of inputs. This collection of representatives is called a multi-agent collective, forming a surrogate model with which an inexpensive computation replaces the original complex task. The mathematical criteria used to derive the collective aim to avoid overlapping of characteristics between representatives, in order to achieve an effective surrogate model and avoid redundancies. The surrogate modeling method is demonstrated on a light inventory that contains light data corresponding to 82 aircraft types. Ten aircraft types are selected by the method to represent the full light inventory for the computation of fuel burn estimates, yielding an error between outputs from the surrogate and full models of just 2.08%. The ten representative aircraft types are selected by first aggregating similar aircraft types together into agents, and then selecting a representative aircraft type for each agent. In assessing the similarity between aircraft types, the characteristic of each aircraft type is determined from available light data instead of solving the fuel burn computation model, which makes the assessment procedure inexpensive.

(cont.) Aggregation criteria are specified to quantify the similarity between aircraft types and a stringency, which controls the tradeoff between the two competing objectives in the modeling -- the number of representatives and the estimation error. The surrogate modeling results are compared to a model obtained via manual aggregation; that is, the aggregation of aircraft types is done based on engineering judgment. The surrogate model derived using the systematic approach yields fewer representatives in the collective, yielding a surrogate model with lower computational cost, while achieving better accuracy. Further, the systematic approach eliminates the subjectivity that is inherent in the manual aggregation method. The surrogate model is also applied to other light inventories, yielding errors of similar magnitude to the case when the reference light inventory is considered.