Active-learning-based non-intrusive Model Order Reduction

TL;DR

This paper introduces an active learning approach for non-intrusive Model Order Reduction that efficiently constructs reduced models using single-time step snapshots and error estimation, enabling fast and versatile digital twin creation.

Contribution

It proposes a novel active learning strategy with a greedy snapshot selection supported by Gaussian Process Regression and a use case-independent validation method based on PAC learning.

Findings

Effective snapshot selection improves model accuracy

Method reduces user interaction and is adaptable across applications

Validated on thermal and furnace models with promising results

Abstract

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).