Hierarchical model reduction driven by machine learning for parametric
advection-diffusion-reaction problems in the presence of noisy data
- URL: http://arxiv.org/abs/2204.00538v1
- Date: Fri, 1 Apr 2022 16:02:05 GMT
- Title: Hierarchical model reduction driven by machine learning for parametric
advection-diffusion-reaction problems in the presence of noisy data
- Authors: Massimiliano Lupo Pasini, Simona Perotto
- Abstract summary: We propose a new approach to generate a reliable reduced model for a parametric elliptic problem in the presence of noisy data.
We show that directional HiPOD looses in terms of accuracy when problem data are affected by noise.
We replace with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant noise.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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