Philipp Bekemeyer

Jigar Parekh, Philipp Bekemeyer

Machine learning models are widely regarded as a way forward to tackle multi-query challenges that arise once expensive black-box simulations such as computational fluid dynamics are investigated. However, ensuring the desired level of accuracy for a certain task at minimal computational cost, e.g. as few black-box samples as possible, remains a challenges. Active learning strategies are used for scalar quantities to overcome this challenges and different so-called infill criteria exists and are commonly employed in several scenarios. Even though needed in various field an extension of active learning strategies towards field predictions is still lacking or limited to very specific scenarios and/or model types. In this paper we propose an active learning strategy for machine learning models that are capable if predicting field which is agnostic to the model architecture itself. For doing so, we combine a well-established Gaussian process model for a scalar reference value and simultaneously aim at reducing the epistemic model error and the difference between scalar and field predictions. Different specific forms of the above-mentioned approach are introduced and compared to each other as well as only scalar-valued based infill. Results are presented for the NASA common research model for an uncertainty propagation task showcasing high level of accuracy at significantly smaller cost compared to an approach without active learning.

Alexander Barklage, Philipp Bekemeyer

Aerodynamic analysis during aircraft design usually involves methods of varying accuracy and spatial resolution, which all have their advantages and disadvantages. It is therefore desirable to create data-driven models which effectively combine these advantages. Such data fusion methods for distributed quantities mainly rely on proper orthogonal decomposition as of now, which is a linear method. In this paper, we introduce a non-linear method based on neural networks combining simulation and measurement data via transfer learning. The network training accounts for the heterogeneity of the data, as simulation data usually features a high spatial resolution, while measurement data is sparse but more accurate. In a first step, the neural network is trained on simulation data to learn spatial features of the distributed quantities. The second step involves transfer learning on the measurement data to correct for systematic errors between simulation and measurement by only re-training a small subset of the entire neural network model. This approach is applied to a multilayer perceptron architecture and shows significant improvements over the established method based on proper orthogonal decomposition by producing more physical solutions near nonlinearities. In addition, the neural network provides solutions at arbitrary flow conditions, thus making the model useful for flight mechanical design, structural sizing, and certification. As the proposed training strategy is very general, it can also be applied to more complex neural network architectures in the future.