Adaptive reduced basis finite element heterogeneous multiscale method

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Deep Multiscale Model Learning (2018, background): “These approximations, e.g., typically involve a form of the coarse-grid equation [2, 23, 4, 22, 14, 7, 10, 21, 1, 20, 25, 26, 43, 41, 30, 13, 15, 11, 12], where the coarse-grid equations are formed and the parameters are computed or found via inverse problems [5, 39, 6, 42, 47].”
High-performance model reduction techniques in computational multiscale homogenization (2014, methodology): “…described, crucial question of how to eﬃciently integrate the resulting reduced-order equations, simply because, in most of them [10,52,26,27,2,1], integration is not an issue — the ﬁne-scale BVPs addressed in these works bear an aﬃne relation with the corresponding coarse-scale, input…”