Table 5 Comparison of different neural network architectures for real manipulator dynamics learning.

From: Symplectic physics-embedded learning via Lie groups Hamiltonian formulation for serial manipulator dynamics prediction

 

PHNODEs

SPEL

SPEL-KAN

M-NN Outputs

171

20

20

V-NN Outputs

1

1

1

D-NN Outputs

171

21

21

G-NN Outputs

18

6

6

Parameters

326,911

156,359

85,521

Activation function

tanh

tanh

learned

Training loss

\(8.13\times 10^{-3}\)

\(7.99\times 10^{-3}\)

\(\varvec{7.96}\times \varvec{10^{-3}}\)

Training time(s)

17.70

3.76

6.44

Test loss

\(9.62\times 10^{-3}\)

\(\varvec{8.77}\times \varvec{10^{-3}}\)

\(9.07\times 10^{-3}\)

  1. 1 -KAN indicates that the internal MLP has been replaced with a KAN.
  2. 2 M-NN Outputs, V-NN Outputs, D-NN Outputs, and G-NN Outputs denote the output nodes of the M-NN, V-NN, D-NN, and G-NN, respectively.
  3. 3 Training time includes the sum of forward computation time and backpropagation time
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