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Advanced Modeling and Simulation in Engineering Sciences

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
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