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DeepBayes—An estimator for parameter estimation in stochastic nonlinear dynamical models
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.ORCID iD: 0000-0001-6612-6923
Automatic Control Laboratory and NCCR Automation, ETH Zürich, Switzerland.
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.ORCID iD: 0000-0003-2638-6047
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Centres, Centre for Advanced BioProduction by Continuous Processing, AdBIOPRO.ORCID iD: 0000-0002-9368-3079
2024 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 159, article id 111327Article in journal (Refereed) Published
Abstract [en]

Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods employ maximum likelihood or Bayesian estimation. However, these methods suffer from some limitations, most notably the substantial computational time for inference coupled with limited flexibility in application. In this work, we propose DeepBayes estimators that leverage the power of deep recurrent neural networks. The method consists of first training a recurrent neural network to minimize the mean-squared estimation error over a set of synthetically generated data using models drawn from the model set of interest. The a priori trained estimator can then be used directly for inference by evaluating the network with the estimation data. The deep recurrent neural network architectures can be trained offline and ensure significant time savings during inference. We experiment with two popular recurrent neural networks — long short term memory network (LSTM) and gated recurrent unit (GRU). We demonstrate the applicability of our proposed method on different example models and perform detailed comparisons with state-of-the-art approaches. We also provide a study on a real-world nonlinear benchmark problem. The experimental evaluations show that the proposed approach is asymptotically as good as the Bayes estimator.

Place, publisher, year, edition, pages
Elsevier Ltd , 2024. Vol. 159, article id 111327
Keywords [en]
Deep learning, Dynamical systems, Nonlinear system identification, Parameter estimation, Recurrent neural networks
National Category
Control Engineering Other Electrical Engineering, Electronic Engineering, Information Engineering Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-339038DOI: 10.1016/j.automatica.2023.111327ISI: 001161034600001Scopus ID: 2-s2.0-85174673962OAI: oai:DiVA.org:kth-339038DiVA, id: diva2:1815513
Note

QC 20231129

Available from: 2023-11-29 Created: 2023-11-29 Last updated: 2024-05-02Bibliographically approved

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Ghosh, AnubhabChatterjee, SaikatHjalmarsson, Håkan

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