Surrogate and Hybrid Models for Control

Bernt Lie
University of South-Eastern Norway, Porsgrunn, Norway

Ladda ner artikelhttps://doi.org/10.3384/ecp201701

Ingår i: Proceedings of The 60th SIMS Conference on Simulation and Modelling SIMS 2019, August 12-16, Västerås, Sweden

Linköping Electronic Conference Proceedings 170:1, s. 1-8

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Publicerad: 2020-01-24

ISBN: 978-91-7929-897-5

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


With access to fast computers and efficient machine learning tools, it is of interest to use machine learning to develop surrogate models from complex physics-based models. Next, a hybrid model is a combination model where a data driven model is built to describe the difference between an imperfect physics-based/surrogate model and experimental data. Availability of Big Data makes it possible to gradually improve on a hybrid model as more data become available. In this paper, an overview is given of relevant ideas from model approximation/data driven models for dynamic systems, and machine learning via artificial neural networks. To illustrate how the ideas can be implemented in practice, a simple introduction to package Flux for language Julia is given. Several types of surrogate models are developed for a simple, illustrative system. Finally, the development of a hybrid model is illustrated. Emphasis is put on ideas related to Digital Twins for control.


digital twin, surrogate models, hybrid models, dynamic systems, control


Peter Benner, Mario Ohlberger, Albert Cohen, and Karen E. Wilcox. Model Reduction and Approximation: Theory and Algorithms. SIAM, Philadelphia, USA, July 2017. ISBN 978-1611974812.

Jeff Bezanson, Alan Edelman, Stefan Karpinski, and Viral B. Sha. Julia: A Fresh Approach to Numerical Computing. SIAM Review, 49(1):65–98, 2017. doi:10.1137/14100067.

Christopher M. Bishop. Neural networks and their applications. Rev. Sci. Instrum., 65(6):1803–1832, June 1994.

Christopher M. Bishop. Pattern Recognition and Machine Learning. Information Science and Statistics. Springer, April 2011. ISBN 978-0387310732.

Stephen Boyd and Lieven Vandenberghe. Introduction to Applied Linear Algebra. Vectors, Matrices, and Least Squares. Cambridge University Press, 2018. ISBN 978-1316518960.

Elías Cueto, David González, and Icíar Alfaro. Proper Generalized Decompositions: An Introduction to Computer Implementation with Matlab. Springer, March 2016. ISBN 978-3319299938.

Abdulmotaleb El Saddik. Digital Twins: The Convergence of Multimedia Technologies. IEEE Multimedia, 25(2):97–92, 2018. ISSN Print ISSN: 1070-986X Electronic ISSN: 1941-0166. doi:10.1109/MMUL.2018.023121167.

Jay A. Farrell and Marios M. Polycarpou. Adaptive Approximation Based Control. Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches. Wiley-Interscience, Hoboken, New Jersey, 2006.

Bruce A. Finlayson. The Method of Weighted Residuals and Variational Principles. Classics in Applied Mathematics. SIAM, Philadelphia, 2014. ISBN 978-1611973235.

Peter Fritzson. Principles of Object-Oriented Modeling and Simulation with Modelica 3.3: A Cyber-Physical Approach. Wiley-IEEE Press, Piscataway, NJ, second edition, 2015. ISBN 978-1-118-85912-4.

Mario Hermann, Tobias Pentek, and Boris Otto. Design Principles for Industrie 4.0 Scenarios. In Proceedings, 2016 49th Hawaii International Conference on System Sciences (HICSS). IEEE, January 2016. doi:10.1109/HICSS.2016.488.

Mike Innes. Flux: Elegant Machine Learning with Julia. Journal of Open Source Software, 2018. doi:10.21105/joss.00602.

Bernt Lie, Arunkumar Palanisamy, Alachew Mengist, Lena Buffoni, Martin Sjölund, Adeel Asghar, Adrian Pop, and Peter Fritzson. OMJulia: An OpenModelica API for Julia-Modelica Interaction. In Proceedings of the 13th International Modelica Conference, pages 699–708, February 2019. doi:10.3384/ecp19157. Regensburg, Germany, March 4–6, 2019.

Zhendong Luo and Goong Chen. Proper Orthogonal Decomposition Methods for Partial Differential Equations. Academic Press, 2018. ISBN 978-0128167984.

Kevin P. Murphy. Machine Learning: A Probabilistic Perspective. Adaptive Computation and Machine Learning. The MIT Press, August 2012. ISBN 978-0262018029.

Christopher Rackauckas and Qing Nie. DifferentialEquations.jl — A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia. Journal of Open Research Software, 5(15), 2017. doi:10.5334/jors.151.

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