Table 1 Validation of the PINN results against RKF-45 findings.

From: Predicting the thermal distribution in a convective wavy fin using a novel training physics-informed neural network method

\({\text{p}}\)

\({\text{X}}\)

\(\Theta\)

PINN

RKF-45

Error

−1/4

0

1.000007

1.000000

7.62939E−06

0.2

0.883129

0.883691

0.000561046

0.4

0.798810

0.799922

0.001111697

0.6

0.734608

0.736249

0.001640231

0.8

0.694266

0.696286

0.002019562

1

0.682647

0.684796

0.002148474

1/4

0

0.999951

1.000000

4.82798E−05

0.2

0.892658

0.892695

3.66471E−05

0.4

0.816564

0.816588

2.36785E−05

0.6

0.759252

0.759288

3.56306E−05

0.8

0.723614

0.723627

1.23073E−05

1

0.713446

0.71347

2.37405E−05

1/3

0

1.000108

1.000000

0.000108004

0.2

0.894164

0.893973

0.000191383

0.4

0.819222

0.818943

0.000279093

0.6

0.762864

0.76253

0.000334411

0.8

0.727856

0.727461

0.000395874

1

0.717921

0.717487

0.000434257

2

0

0.999963

1.000000

3.61204E−05

0.2

0.912096

0.912148

5.16784E−05

0.4

0.852048

0.85211

6.13645E−05

0.6

0.807671

0.807757

8.52146E−05

0.8

0.780521

0.780621

9.9786E−05

1

0.772955

0.773073

0.000117642

3

0

0.999983

1.000000

1.62721E−05

0.2

0.919179

0.919204

2.42028E−05

0.4

0.864789

0.864811

2.16333E−05

0.6

0.824819

0.824861

4.14948E−05

0.8

0.800506

0.800555

4.8289E−05

1

0.793797

0.793862

6.44474E−05

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