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Advanced Modeling and Simulation in Engineering Sciences

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
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