This work presents an a priori MOR strategy where the multidimensional model equations, with some parameters set as new variables of the problem, are solved. Neither SVD nor previous precomputed solutions are used to build the surrogate model. Instead, the proper generalized decomposition (PGD) is applied. More precisely, the generalized solution is a priori represented using products of separated functions defined in low-dimensional spaces. Each of these functions is evaluated within a greedy algorithm and a Gauss-Seidel approach during the offline phase, reducing the high-dimensional complexity of the original equations. Compared to POD-based methods, multiple crucial benefits appear when using a PGD approximation: (i) a database of solutions for realistic applications is available to the user for any required combination of parameter values, (ii) the access to this database is immediate, and (iii) inversion techniques can be drastically accelerated since all the derivatives with respect to any parameter are also readily available.


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  1. Ammar, A., Mokdad, B., Chinesta, F. and Keunings, R.
    [2006] A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. J. Non-Newtonian Fluid Mech., 139, 153–176.
    [Google Scholar]
  2. [2007] A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Part II: transient simulation using space-time separated representations. J. Non-Newtonian Fluid Mech., 144, 98–121.
    [Google Scholar]
  3. Baysal, E., Kosloff, D.D. and Sherwood, J.W.
    [1983] Reverse time migration. Geophysics, 48(11), 1514–1524.
    [Google Scholar]
  4. Fernández-Martínez, J.L.
    [2015] Model reduction and uncertainty analysis in inverse problems. The Leading Edge, 34(9), 1006–1016.
    [Google Scholar]
  5. Modesto, D., Zlotnik, S. and Huerta, A.
    [2015] Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation. Com-put. Methods Appl. Mech. Eng., 295, 127–149.
    [Google Scholar]
  6. Nouy, A.
    [2010] A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations. Comput. Methods Appl. Mech. Eng., 199, 1603–1626.
    [Google Scholar]
  7. Pereyra, V.
    [2016] Model order reduction with oblique projections for large scale wave propagation. Journal of Computational and Applied Mathematics, 295, 103–114. {VIII} Pan-American Workshop in Applied and Computational Mathematics.
    [Google Scholar]
  8. Pratt, R.G.
    [1999] Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model. Geophysics, 64, 888–901.
    [Google Scholar]
  9. Virieux, J. and Operto, S.
    [2009] An overview of full-waveform inversion in exploration geophysics. Geophysics, 74, WCC127–WCC152.
    [Google Scholar]
  10. Zaslavsky, M., Druskin, V. and Mamonov, A.V.
    [2015] Multiscale Mimetic Reduced-Order Models for Spectrally Accurate Wavefield Simulations. In: 2015 SEG Annual Meeting. Society of Exploration Geophysicists.
    [Google Scholar]

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