Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data - Archive ouverte HAL Access content directly
Journal Articles Journal of Scientific Computing Year : 2023

Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data

Massimiliano Lupo Pasini

Abstract

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.

Dates and versions

hal-03928984 , version 1 (08-01-2023)

Identifiers

Cite

Massimiliano Lupo Pasini, Simona Perotto. Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data. Journal of Scientific Computing, 2023, 94 (2), pp.36. ⟨10.1007/s10915-022-02073-6⟩. ⟨hal-03928984⟩
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