Machine learning approaches are currently used to understand or model complex physical systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data is often relatively time-consuming or expensive. Moreover, the problems of industrial interest tend to be more and more complex, and depend on a high number of parameters. High-dimensional problems intrinsically involve the need for large amounts of data through the curse of dimensionality. That is why new approaches based on smart sampling techniques have been investigated to minimize the number of samples to be given to train the model, such as active learning methods. Here, we propose a technique based on a combination of the Fisher information matrix and sparse proper generalized decomposition that enables the definition of a new active learning informativeness criterion in high dimensions. We provide examples proving the performances of this technique on a theoretical 5D polynomial function and on an industrial crash simulation application. The results prove that the proposed strategy outperforms the usual ones.

Machine learning approaches are currently used to understand or model complex physical systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data is often relatively time-consuming or expensive. Moreover, the problems of industrial interest tend to be more and more complex and depending on a high number of parameters. High dimensional problems intrinsically involve the need of large data amount through the curse of dimensionality. That is why, new approaches based on smart sampling techniques are investigated to minimize the number of samples to be given to train the model, such as Active Learning methods. Here, we propose a technique based on a combination of Fisher information matrix and of Sparse Proper Generalized Decomposition that enables the definition of a new Active Learning informativeness criterion in high dimensions. We provide examples proving the performances of this technique on a theoretical 5D polynomial function and on an industrial crash simulation application. The results prove that the proposed strategy over-perform the usual ones.

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.