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Table 2 Comparison of different machine learning methods using 4th-order Runge–Kutta for 1D inviscid Burgers’ 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 1.854 0.0309 2.42e−3
SVR 3 1.744 0.0310 2.42e−3
SVR rbf 1.773 0.0321 5.03e−3
Random Forest 6.513 0.0817 0.0726
Boosting 10.076 0.0904 0.0858
kNN 0.244 0.0467 0.0336
VKOGA 0.058 0.0353 0.0164
SINDy 0.063 0.0310 2.42e−3
Galerkin 0.194 0.0304 0
  1. The running time of FOM and Galerkin is 0.401s and 0.194s respectively
  2. Bold values indicate the models selected with smallest online running time, or relative error w.r.t. FOM and/or ROM