Active-learning-based non-intrusive Model Order Reduction
This work addresses the challenge of efficient snapshot selection in non-intrusive MOR for industrial applications like Digital Twins, though it appears incremental as it builds on existing active learning and error estimation methods.
The paper tackles the problem of constructing good snapshot sets for non-intrusive Model Order Reduction by proposing an active learning approach with a greedy strategy and error estimator, tested on 2-D thermal conduction and 3-D vacuum furnace models, showing potential for industrial Digital Twins with minimal user interaction.
The Model Order Reduction (MOR) technique can provide compact numerical models for fast simulation. Different from the intrusive MOR methods, the non-intrusive MOR does not require access to the Full Order Models (FOMs), especially system matrices. Since the non-intrusive MOR methods strongly rely on the snapshots of the FOMs, constructing good snapshot sets becomes crucial. In this work, we propose a new active learning approach with two novelties. A novel idea with our approach is the use of single-time step snapshots from the system states taken from an estimation of the reduced-state space. These states are selected using a greedy strategy supported by an error estimator based Gaussian Process Regression (GPR). Additionally, we introduce a use case-independent validation strategy based on Probably Approximately Correct (PAC) learning. In this work, we use Artificial Neural Networks (ANNs) to identify the Reduced Order Model (ROM), however the method could be similarly applied to other ROM identification methods. The performance of the whole workflow is tested by a 2-D thermal conduction and a 3-D vacuum furnace model. With little required user interaction and a training strategy independent to a specific use case, the proposed method offers a huge potential for industrial usage to create so-called executable Digital Twins (DTs).