Overlapping clustering based technique for scalable uncertainty quantification in physical systems

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

Research output: Contribution to journalArticlepeer-review


Forward propagation of uncertainty in physics-based model is nontrivial and a necessary undertaking. This paper provides a methodology for decomposing the state space of scalable dynamical systems with strong interstate coupling. The outlined approach intends to make rigorous Uncertainty Quantification (UQ) of the high-dimension problem feasible by partitioning the overall high-dimensional state space problem into multiple lower-dimensional state space problems. This approach will work quicker with a lesser memory space requirement than existing methods. To enable accelerated and scalable UQ in high-dimensional complex physical system models, the proposed decomposition process leverages an overlapping community detection to detect state variables participating in more than one subsystems (clusters). The final UQ solution is obtained by using the concept of Hadamard product of the state variables in a subsystem (cluster) and their association in the cluster. The developed approach has been tested to detect connected subsystems in coupled dynamical systems. The results analyzing spatio-temporal flow equation are also presented. It is also shown that proposed framework approach is faster and works with a lesser memory requirement to carry out UQ of high-dimensional physical system models.

Original languageEnglish (US)
Pages (from-to)827-859
Number of pages33
JournalSIAM-ASA Journal on Uncertainty Quantification
Issue number3
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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