Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction
This work addresses the challenge of improving accuracy in reduced-order models for transport and turbulent flow problems, representing an incremental advancement in domain-specific computational methods.
The paper tackles the problem of training quadratic manifolds for nonintrusive model reduction by proposing a greedy procedure that minimizes both reconstruction and prediction errors, leading to reduced models with up to two orders of magnitude higher accuracy compared to methods focusing only on reconstruction error.
Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to the embedded data in downstream learning steps is ignored. In contrast, we propose a greedy training procedure that takes into account both the reconstruction error on the snapshot data and the prediction error of reduced models fitted to the data. Because our procedure learns quadratic manifolds with the objective of achieving accurate reduced models, it avoids oscillatory and other non-smooth embeddings that can hinder learning accurate reduced models. Numerical experiments on transport and turbulent flow problems show that quadratic manifolds trained with the proposed greedy approach lead to reduced models with up to two orders of magnitude higher accuracy than quadratic manifolds trained with respect to the reconstruction error alone.