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

Advanced Modeling and Simulation in Engineering Sciences

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)

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

The running time of FOM and Galerkin is 209.393s and 16.837s respectively
Bold values indicate the models selected with smallest online running time, or relative error w.r.t. FOM and/or ROM