Optimized Active Learning Method for High-Dimensional Industrial Regression Problems

Machine learning approaches are commonly used to model physical phenomena due to their adaptability to complex systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data points is often costly. Moreover, high-dimensional problems inherently require large amounts of data due to the curse of dimensionality. That is why new approaches based on smart sampling techniques are being investigated to optimize the acquisition of training samples, such as active learning methods. Initialization is a crucial step in active learning as it influences both performance and computational cost. Moreover, the scenarios used to select the next sample, such as classic pool-based sampling, can be highly resource- and time consuming. This study focuses on optimizing active learning methods through a comprehensive analysis of initialization strategies and scenario design, proposing and evaluating multiple approaches to determine the optimal configurations. The methods are applied to high-dimensional industrial problems with dimensions ranging from 5 to 15, where challenges associated with high dimensionality are already significant. To address this, the proposed study uses an active learning criterion that combines Sparse Proper Generalized Decomposition with Fisher information theory, specifically tailored to high-dimensional industrial settings. We illustrate the effectiveness of these techniques through examples on theoretical 5D and 15D functions, as well as a practical industrial crash simulation application.