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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)

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