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Order Reduction for Uncertainty Quantification of Dynamical Systems

Theory-Algorithms

  • S. Mowlavi, T. Sapsis, Model order reduction for stochastic dynamical systems with continuous symmetriesSIAM Journal on Scientific Computing40 (2018) 1669-1695. [pdf]
  • T. Sapsis, A. Majda, Statistically accurate low order models for uncertainty quantification in turbulent dynamical systemsProceedings of the National Academy of Sciences110 (2013) 13705-13710.[pdf]
  • T. Sapsis, A. Majda, Blending modified Gaussian closure and non-Gaussian reduced subspace methods for turbulent dynamical systemsJournal of Nonlinear Science23 (2013) 1039 (33 pages). [pdf]
  • T. Sapsis, A. Majda, Blended reduced subspace algorithms for uncertainty quantification of quadratic systems with a stable mean statePhysica D258 (2013) 61-76. [pdf]
  • T. Sapsis, Attractor local dimensionality, nonlinear energy transfers, and finite-time instabilities in stochastic dynamical systems with applications to 2D fluid flowsProceedings of the Royal Society A469 (2013) 20120550 (23 pages). [pdf]
  • T. Sapsis & P. Lermusiaux, Dynamical criteria for the evolution of the stochastic dimensionality in flows with uncertaintyPhysica D241 (2012) 60-76. [pdf]
  • T. Sapsis & P. Lermusiaux, Dynamically orthogonal field equations for continuous stochastic dynamical systemsPhysica D238 (2009) 2347-2360. [pdf]

Applications

  • H. Babaee, M. Choi, T. Sapsis, G. KarniadakisA robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problemsJournal of Computational Physics344 (2017) 303-319. [pdf].
  • M. Choi, T. Sapsis, G. E. Karniadakis, On the equivalence of dynamically orthogonal and dynamically bi-orthogonal methods: Theory and numerical simulationsJournal of Computational Physics270 (2014) 1-20. [pdf]
  • M. Ueckermann, P. Lermusiaux, T. Sapsis, Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flowsJournal of Computational Physics233 (2013) 272-294. [pdf]
  • T. Sapsis, and H. A. Dijkstra, Interaction of additive noise and nonlinear dynamics in the double-gyre wind-driven ocean circulationJournal of Physical Oceanography43 (2013) 366-381. [pdf]
  • T. Sapsis, M. Ueckermann, P. Lermusiaux, Global analysis of Navier-Stokes and Boussinesq stochastic flows using dynamical orthogonalityJournal of Fluid Mechanics734 (2013) 83-113. [pdf]
  • M. Choi, T. Sapsis, G. E. Karniadakis, A convergence study for SPDEs using combined polynomial chaos and dynamically-orthogonal schemesJournal of Computational Physics245 (2013) 281-301. [pdf]