Goal-Driven Adaptive Sampling Strategies for Machine Learning Models Predicting Fields

• A model-agnostic active learning strategy for field predictions that extends classical infill criteria beyond scalar outputs. • A unified scalar–field surrogate training framework that jointly reduces epistemic uncertainty and enforces consistency between global coefficients and distributed values. • Significant accuracy gains at reduced computational cost, demonstrated on the NASA Common Research Model for uncertainty propagation. 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 challenge. Active learning strategies are used for scalar quantities to overcome this challenge and different so-called infill criteria exist and are commonly employed in several scenarios. Even though needed in various fields, 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 of predicting fields, 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.