Goal-Oriented Active Learning with Local Model Networks

Goal-Oriented Active Learning with Local Model Networks

Julian Belz Konrad Bamberger | Oliver Nelles Thomas Carolus

Institute of Mechanics and Control Engineering, University of Siegen, Germany

Institute of Fluid- and Thermodynamics, University of Siegen, Germany

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A methodology for goal-oriented active learning with local model networks (LMNs) is proposed. It is applied for the generation of training data for a computational fluid dynamics (CFD) metamodel. The used metamodel is an LMN trained with data originating from CFD simulations. This metamodel describes the total-to-static efficiency for a given design point, defined by the pressure rise at a specific volume flow rate, depending on geometrical parameters of an impeller of centrifugal fans. The goal- oriented nature originates from three main targets that are addressed simultaneously during the active learning procedure. (I) The concentration on possibly optimal geometries and (II) the focus on areas in the input space where the metamodel’s performance is considered to be worst. Additionally, (III) new measurements should differ from already simulated geometries as much as possible. With these goals three important issues in modeling are addressed simultaneously: (I) optimality, (II) model bias, (III) model variance/uniformly space-filling property. In order to fulfill all goals, special properties of LMNs are utilized (embedded approach). Through the structure of LMNs, it is possible to assign local model errors to specific areas in the input space. New measurements are preferably placed in such high-error regions, while concentrating on presumably optimal geometries that differ most from the ones already available in the training data. In the field of fluid machinery, the range of achievable design points is usually identified by the Cordier diagram. While the design points obtained in the passive learning phase fairly agree with the standard Cordier diagram, an extension of achievable design points was observed due to the proposed goal-oriented learning strategy. In addition, the total-to-static efficiency could be improved in some areas of the Cordier diagram.


active learning, aerodynamic optimization, design of experiments, experimental modeling, impeller of centrifugal fans, metamodeling


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