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Table 10 Statistical error analysis of PINNs results for different values of time variable t to Example 4.2

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

t

MAE

MSE

Range

Variance

Standard deviation

0.0

5.291e−06

9.161e−11

1.467e−05

3.905e−12

2.588e−06

0.1

5.571e−06

9.268e−11

2.114e−05

4.231e−12

2.620e−06

0.2

5.807e−06

9.439e−11

2.127e−05

4.547e−12

2.613e−06

0.3

5.968e−06

9.541e−11

2.130e−05

5.101e−12

2.674e−06

0.4

6.132e−06

9.418e−11

2.150e−05

5.145e−12

2.715e−06

0.5

6.978e−06

9.588e−11

2.853e−05

6.015e−12

2.757e−06

0.6

7.430e−06

9.641e−11

2.867e−05

7.823e−12

2.782e−06

0.7

7.907e−06

9.525e−11

3.045e−05

7.932e−12

2.858e−06

0.8

8.231e−06

9.669e−11

3.116e−05

8.807e−12

2.887e−06

0.9

9.305e−06

9.670e−11

3.540e−05

8.964e−12

3.341e−06

1.0

9.796e−06

9.688e−11

3.617e−05

9.731e−12

3.518e−06