Local Lagrangian reduced-order modeling for the Rayleigh-Taylor instability by solution manifold decomposition

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“…The results in Figs. 10,11,12, and 13 of Appendix A.1.2 in [31] indicate similar results across all methods with no noise. For a noisy measurement case described in Section 3, the uniform sampling method yields the most accurate results.…”

“…In the Gappy AE method, data is reconstructed using a nonlinear manifold by training the auto-encoder. Unlike a linear subspace-based approach, such as the Gappy POD method, the Gappy AE shows O (10) to O(100) times less data reconstruction error when assuming noiseless measurement. The superior representability of the nonlinear manifold allows the Gappy AE to reconstruct gappy data when known (measured) data is sparse.…”

“…26, 27, and 28 of Appendix B in [31]. Gappy AE is O (10) to O(100) times more accurate than the Gappy POD in terms of projection error. The projection errors without noise are slightly lower than those with noise; the effects of noise in computing projection errors are negligible.…”

“…In intrusive methods, the governing equations are solved with a substituted solution approximation. Projection-based reduced-order models, such as the linear subspace reduced-order model [7,16,12,15,17,10], nonlinear manifold reduced-order model [36,30,29,19], component-wise reducedorder model [38,39] and space-time reduced-order model [14,13,32,47], are examples of intrusive methods. These techniques are widely employed to expedite physical simulations.…”