Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling

TL;DR

This paper enhances reduced basis surrogate models for parametrized PDEs by integrating advanced deep kernel machine learning techniques, improving efficiency and adaptability in numerical simulations.

Contribution

It introduces novel structured deep kernel networks into the RB-ML-ROM framework, advancing surrogate modeling capabilities for parametrized PDEs.

Findings

Enhanced surrogate accuracy with deep kernel models

Improved efficiency in numerical experiments

Demonstrated benefits of structured kernel models

Abstract

In the framework of reduced basis methods, we recently introduced a new certified hierarchical and adaptive surrogate model, which can be used for efficient approximation of input-output maps that are governed by parametrized partial differential equations. This adaptive approach combines a full order model, a reduced order model and a machine-learning model. In this contribution, we extend the approach by leveraging novel kernel models for the machine learning part, especially structured deep kernel networks as well as two layered kernel models. We demonstrate the usability of those enhanced kernel models for the RB-ML-ROM surrogate modeling chain and highlight their benefits in numerical experiments.