Non-negative Matrix Factorization based uncertainty quantification method for complex networked systems

Arpan Mukherjee, Rahul Rai, Puneet Singla, Tarunraj Singh, Abani Patra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The behavior of large networked systems with underlying complex nonlinear dynamic are hard to predict. With increasing number of states, the problem becomes even harder. Quantifying uncertainty in such systems by conventional methods requires high computational time and the accuracy obtained in estimating the state variables can also be low. This paper presents a novel computational Uncertainty Quantifying (UQ) method for complex networked systems. Our approach is to represent the complex systems as networks (graphs) whose nodes represent the dynamical units, and whose links stand for the interactions between them. First, we apply Non-negative Matrix Factorization (NMF) based decomposition method to partition the domain of the dynamical system into clusters, such that the inter-cluster interaction is minimized and the intra-cluster interaction is maximized. The decomposition method takes into account the dynamics of individual nodes to perform system decomposition. Initial validation results on two well-known dynamical systems have been performed. The validation results show that uncertainty propagation error quantified by RMS errors obtained through our algorithms are competitive or often better, compared to existing methods.

Original languageEnglish (US)
Title of host publication41st Design Automation Conference
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791857076
DOIs
StatePublished - Jan 1 2015
EventASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015 - Boston, United States
Duration: Aug 2 2015Aug 5 2015

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume2A-2015

Other

OtherASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015
CountryUnited States
CityBoston
Period8/2/158/5/15

Fingerprint

Uncertainty Quantification
Non-negative Matrix Factorization
Factorization
Decomposition
Dynamical systems
Decomposition Method
Dynamical system
Interaction
RMS Errors
Uncertainty Propagation
Uncertainty
Large scale systems
Complex Dynamics
Vertex of a graph
Nonlinear Dynamics
Complex Systems
Partition
Decompose
Predict
Unit

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Cite this

Mukherjee, A., Rai, R., Singla, P., Singh, T., & Patra, A. (2015). Non-negative Matrix Factorization based uncertainty quantification method for complex networked systems. In 41st Design Automation Conference (Proceedings of the ASME Design Engineering Technical Conference; Vol. 2A-2015). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC201546087
Mukherjee, Arpan ; Rai, Rahul ; Singla, Puneet ; Singh, Tarunraj ; Patra, Abani. / Non-negative Matrix Factorization based uncertainty quantification method for complex networked systems. 41st Design Automation Conference. American Society of Mechanical Engineers (ASME), 2015. (Proceedings of the ASME Design Engineering Technical Conference).
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Mukherjee, A, Rai, R, Singla, P, Singh, T & Patra, A 2015, Non-negative Matrix Factorization based uncertainty quantification method for complex networked systems. in 41st Design Automation Conference. Proceedings of the ASME Design Engineering Technical Conference, vol. 2A-2015, American Society of Mechanical Engineers (ASME), ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015, Boston, United States, 8/2/15. https://doi.org/10.1115/DETC201546087

Non-negative Matrix Factorization based uncertainty quantification method for complex networked systems. / Mukherjee, Arpan; Rai, Rahul; Singla, Puneet; Singh, Tarunraj; Patra, Abani.

41st Design Automation Conference. American Society of Mechanical Engineers (ASME), 2015. (Proceedings of the ASME Design Engineering Technical Conference; Vol. 2A-2015).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Mukherjee A, Rai R, Singla P, Singh T, Patra A. Non-negative Matrix Factorization based uncertainty quantification method for complex networked systems. In 41st Design Automation Conference. American Society of Mechanical Engineers (ASME). 2015. (Proceedings of the ASME Design Engineering Technical Conference). https://doi.org/10.1115/DETC201546087