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Table 4 Comparison of different machine learning methods using 4th-order Runge–Kutta for 2D convection–diffusion equation

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 1.850 0.0087 0.0076
SVR 3 1.740 0.0065 0.0052
SVR rbf 1.777 0.0185 0.0174
Random Forest 20.313 0.0426 0.0419
Boosting 32.668 0.0177 0.0166
kNN 0.175 0.0153 0.0146
VKOGA 0.041 0.0083 0.0069
SINDy 0.055 0.0077 0.0066
Galerkin 19.012 0.0029 0
  1. The running time of FOM and Galerkin is 138.319s and 19.012s respectively
  2. Bold values indicate the models selected with smallest online running time, or relative error w.r.t. FOM and/or ROM