A Robust Learning Methodology for Uncertainty-Aware Scientific Machine Learning Models

Erbet Almeida Costa, Carine de Menezes Rebello, Márcio Fontana, Leizer Schnitman and Idelfonso Bessa dos Reis Nogueira ()
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Erbet Almeida Costa: Programa de Pós-Graduação em Mecatrônica, Universidade Federal da Bahia, Rua Prof. Aristides Novis, 2, Federação, Salvador 40210-630, Brazil
Carine de Menezes Rebello: Programa de Pós-Graduação em Engenharia Industrial, Universidade Federal da Bahia, Rua Prof. Aristides Novis, 2, Federação, Salvador 40210-630, Brazil
Márcio Fontana: Programa de Pós-Graduação em Mecatrônica, Universidade Federal da Bahia, Rua Prof. Aristides Novis, 2, Federação, Salvador 40210-630, Brazil
Leizer Schnitman: Programa de Pós-Graduação em Mecatrônica, Universidade Federal da Bahia, Rua Prof. Aristides Novis, 2, Federação, Salvador 40210-630, Brazil
Idelfonso Bessa dos Reis Nogueira: Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway

Mathematics, 2022, vol. 11, issue 1, 1-24

Abstract: Robust learning is an important issue in Scientific Machine Learning (SciML). There are several works in the literature addressing this topic. However, there is an increasing demand for methods that can simultaneously consider all the different uncertainty components involved in SciML model identification. Hence, this work proposes a comprehensive methodology for uncertainty evaluation of the SciML that also considers several possible sources of uncertainties involved in the identification process. The uncertainties considered in the proposed method are the absence of a theory, causal models, sensitivity to data corruption or imperfection, and computational effort. Therefore, it is possible to provide an overall strategy for uncertainty-aware models in the SciML field. The methodology is validated through a case study developing a soft sensor for a polymerization reactor. The first step is to build the nonlinear model parameter probability distribution (PDF) by Bayesian inference. The second step is to obtain the machine learning model uncertainty by Monte Carlo simulations. In the first step, a PDF with 30,000 samples is built. In the second step, the uncertainty of the machine learning model is evaluated by sampling 10,000 values through Monte Carlo simulation. The results demonstrate that the identified soft sensors are robust to uncertainties, corroborating the consistency of the proposed approach.

Keywords: scientific machine learning; robust learning; uncertainty; Markov Chain Monte Carlo (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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