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Table 3 Comparison of different machine learning methods using the Backward Euler integrator for 2D convection–diffusion equation: Newton’s method (N); FP-fixed-point iteration (FP)

From: Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

Method Online running time (s) R Err (w.r.t. FOM) R Err (w.r.t. Galerkin)
SVR 2 FP 13.510 0.0074 0.0061
SVR 2 N 10.510 0.0074 0.0061
SVR 3 FP 13.873 0.0045 0.0028
SVR 3 N 10.135 0.0045 0.0028
SVR rbf FP 13.349 0.0181 0.0169
SVR rbf N 10.405 0.0181 0.0169
Random Forest 120.674 0.0332 0.0326
Boosting 190.632 0.0147 0.0135
kNN 0.435 0.0149 0.0142
VKOGA FP 2.505 0.0059 0.0041
VKOGA N 0.151 0.0059 0.0041
SINDy FP 0.534 0.0066 0.0054
SINDy N 0.236 0.0066 0.0054
Galerkin 0.942 0.0029 0
  1. The running time of FOM and Galerkin is 209.393s and 16.837s respectively
  2. Bold values indicate the models selected with smallest online running time, or relative error w.r.t. FOM and/or ROM