An adaptive model hierarchy for data-augmented training of kernel models for reactive flow

TL;DR

This paper introduces an adaptive hierarchy of reduced basis models to efficiently generate training data for kernel models in simulating time-dependent reactive flows governed by PDEs, reducing computational costs.

Contribution

It presents a novel adaptive hierarchy of reduced basis models to augment training data for kernel models in complex PDE simulations.

Findings

Efficient generation of training data for kernel models.

Reduced computational cost for large-scale simulations.

Validated approach for reactive flow modeling.

Abstract

We consider machine-learning of time-dependent quantities of interest derived from solution trajectories of parabolic partial differential equations. For large-scale or long-time integration scenarios, where using a full order model (FOM) to generate sufficient training data is computationally prohibitive, we propose an adaptive hierarchy of intermediate Reduced Basis reduced order models (ROM) to augment the FOM training data by certified ROM training data required to fit a kernel model.