Low-rank methods for high-dimensional approximation and model order reduction

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POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition (2021, methodology): “, and P(F) = F(2E+ tr(E)I) is the rst Piola-Kirchho stress tensor. Here n = 2 parameters are considered, given by the Young modulus 1 and the Poisson ratio 2, belonging to the parameter space P= [1;3] Pa [0:25;0:42]; they aect the expression of the Lame coecients as follows = 1 2(1 + 1) and = 12 (1 ”
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data (2019, background): “, proper orthogonal decomposition (POD, also known as principal component analysis) [3], and the full-order PDE operator is projected onto the subspace spanned by the reduced basis.”
A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs (2020, background): “Hence, no matter whether the PDE is linear or not, the resulting ROM is linear since the reduced dynamics is obtained through a projection onto a linear subspace [2, 3, 4].”