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

Advanced Modeling and Simulation in Engineering Sciences

Table 1 Comparison of different machine learning methods using backward Euler methods for 1D inviscid Burgers’ equation: Newton’s method (N); fixed-point iteration (FP)

Method	Online running time (s)	R Err (w.r.t. FOM)	R Err (w.r.t. Galerkin)
SVR 2 FP	93.365	0.0346	1.62e−4
SVR 2 N	53.772	0.0346	1.62e−4
SVR 3 FP	102.873	0.0346	1.02e−5
SVR 3 N	78.935	0.0346	1.02e−5
SVR rbf FP	104.349	0.0353	8.12e−3
SVR rbf N	104.548	0.0353	8.12e−3
Random Forest	374.201	0.0756	0.0638
Boosting	587.473	0.0980	0.0873
kNN	1.108	0.0558	0.0427
VKOGA FP	2.505	0.0365	0.0122
VKOGA N	1.217	0.0365	0.0122
SINDy FP	0.534	0.0346	4.36e−5
SINDy N	0.373	0.0346	4.36e−5
Galerkin	0.942	0.0346	0

The running time of FOM and Galerkin is 3.886s and 0.942s respectively
Bold values indicate the models selected with smallest online running time, or relative error w.r.t. FOM and/or ROM