InterPore2023

Dynamic Mode Decomposition for model reduction of flow and transport in porous media

22 May 2023, 11:20

15m

Oral Presentation (MS14) Uncertainty Quantification in Porous Media MS14

Speaker

Valentina Ciriello (University of Bologna)

Description

Reduced-order models (ROMs) can be used in place of a high-fidelity model (HFM) to alleviate the computational cost associated with HFM simulations. Emulators or surrogates are a class of ROMs whose aim is to reduce the complexity of a given HFM by learning the dynamics of the state variables directly from the model’s output, i.e. they are trained on a dataset generated by running the HFM multiple times. As such, the number of simulations required to train a ROM is a measure of its effectiveness. Here, we use dynamic mode decomposition (DMD), a powerful data-driven method to construct ROMs of complex dynamical systems [1,2]. DMD employs singular value decomposition (SVD) and pursues the computation of the best-fit linear operator to approximate the relationship between time-shifted snapshots in time of the state variable [2]. Variants of the standard DMD algorithm exist, including the residual, generalized, and extended DMD [2,3]. In this study, we assess the accuracy of different DMD algorithms when mimicking flow and transport in porous media. We consider both interpolation and extrapolation (i.e. to get short-time future prediction) scenarios. The DMD has proven its utility in approximating systems of partial differential equations (PDEs); however, it doesn’t handle the possible variability in model parameters. As such, we explore how to combine DMD with the Polynomial Chaos Expansion (PCE), a family of ROMs used to approximate the response surface of a HFM in the random parameter space; this allows to obtain a ROM in terms of a polynomial relationship explaining the model response of interest as a function of the uncertain parameters, properly represented as independent random variables [4,5].

References

[1] P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, 2010, Journal of Fluid Mechanics 656:5–28. doi:10.1017/s0022112010001217.
[2] J. N. Kutz, S. L. Brunton, B. W. Brunton, J. L. Proctor, Dynamic Mode Decomposition, 2016, Society for Industrial and Applied Mathematics. doi:10.1137/1.9781611974508.
[3] H. Lu, D. M. Tartakovsky, Extended dynamic mode decomposition for inhomogeneous problems, 2021, Journal of Computational Physics 444:110550. doi:10.1016/j.jcp.2021.110550.
[4] R.G. Ghanem, P.D. Spanos, 1991, Stochastic Finite Elements - A Spectral Approach. Springer, Berlin.
[5] V. Ciriello, V. Di Federico, M. Riva, F. Cadini, J. De Sanctis, E. Zio, A. Guadagnini, 2013, Polynomial chaos expansion for global sensitivity analysis applied to a model of radionuclide migration in a randomly heterogeneous aquifer. Stochastic Environmental Research and Risk Assessment, 27:945–954. doi:10.1007/s00477-012-0616-7.