Hierarchical model reduction driven by machine learning for parametric advection-diffusion-reaction problems in the presence of noisy data

TL;DR

This paper introduces a machine learning-enhanced hierarchical model reduction technique for parametric advection-diffusion-reaction problems, effectively handling noisy data by replacing interpolation with data-driven fitting.

Contribution

It presents a novel integration of machine learning with hierarchical model reduction to improve accuracy in noisy data scenarios, extending the directional HiPOD method.

Findings

Machine learning fitting improves model accuracy with noisy data.

The approach effectively discriminates physical features from noise.

Preliminary numerical results confirm potential benefits.

Abstract

We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.