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Table 4 PINNs approximation errors along with train and test losses for different hidden layers

From: A deep learning approach: physics-informed neural networks for solving a nonlinear telegraph equation with different boundary conditions

Hidden layer

\(L_{2}\)

\(L_{\infty }\)

RMSE

Train loss

Test loss

1

1.137e−04

2.661e−04

1.138e−04

1.18e−07

1.49e−07

2

8.028e−05

2.110e−04

7.01e−05

6.09e−08

5.87e−08

3

1.218e−05

3.527e−05

1.269e−05

9.53e−10

1.13e−09

4

3.382e−05

8.794e−05

3.382e−05

1.00e−09

1.04e−09

5

7.499e−06

7.233e−06

1.720e−05

8.27e−10

8.58e−10

6

2.116e−05

5.185e−05

1.919e−05

2.58e−09

2.74e−09

7

4.596e−05

1.262e−04

4.409e−05

1.26e−09

1.08e−09