A methodology to assess and improve the physics consistency of an artificial neural network regression model for engineering applications

Rajasekhar Nicodemus, E.

doi:10.1186/s40323-022-00224-w

Advanced Modeling and Simulation in Engineering Sciences

Table 4 Development points and expected region of approximation

From: A methodology to assess and improve the physics consistency of an artificial neural network regression model for engineering applications

Development point	Expected region of approximation	Maximum absolute error
[0.4333, 0.45, 0.45, 0.5, 0.5]	x₁ϵ [0.4, 0.4667], x₂ϵ [0.4, 0.5], x₃ϵ [0.4, 0.5], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.003518
[0.4333, 0.45, 0.55, 0.5, 0.5]	x₁ϵ [0.4, 0.4667], x₂ϵ [0.4, 0.5], x₃ϵ [0.5, 0.6], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.003519
[0.4333, 0.55, 0.45, 0.5, 0.5]	x₁ϵ [0.4, 0.4667], x₂ϵ [0.5, 0.6], x₃ϵ [0.4, 0.5], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.004026
[0.4333, 0.55, 0.55, 0.5, 0.5]	x₁ϵ [0.4, 0.4667], x₂ϵ [0.5, 0.6], x₃ϵ [0.5, 0.6], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.002399
[0.5, 0.45, 0.45, 0.5, 0.5]	x₁ϵ [0.4667,0.5333], x₂ϵ [0.4, 0.5], x₃ϵ [0.4, 0.5], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.003433
[0.5, 0.45, 0.55, 0.5, 0.5]	x₁ϵ [0.4667,0.5333], x₂ϵ [0.4, 0.5], x₃ϵ [0.5, 0.6], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.007536
[0.5, 0.55, 0.45, 0.5, 0.5]	x₁ϵ [0.4667,0.5333], x₂ϵ [0.5, 0.6], x₃ϵ [0.4, 0.5], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.010849*
[0.5, 0.55, 0.55, 0.5, 0.5]	x₁ϵ [0.4667,0.5333], x₂ϵ [0.5, 0.6], x₃ϵ [0.5, 0.6], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.009431
[0.5667, 0.45, 0.45, 0.5, 0.5]	x₁ϵ [0.5333,0.6], x₂ϵ [0.4, 0.5], x₃ϵ [0.4, 0.5], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.004257
[0.5667, 0.45, 0.55, 0.5, 0.5]	x₁ϵ [0.5333,0.6], x₂ϵ [0.4, 0.5], x₃ϵ [0.5, 0.6], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.003938
[0.5667, 0.55, 0.45, 0.5, 0.5]	x₁ϵ [0.5333,0.6], x₂ϵ [0.5, 0.6], x₃ϵ [0.4, 0.5], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.005373
[0.5667, 0.55, 0.55, 0.5, 0.5]	x₁ϵ [0.5333,0.6], x₂ϵ [0.5, 0.6], x₃ϵ [0.5, 0.6], x₄ϵ [0.4,0.6], x₅ϵ [0.4,0.6]	0.003434

Back to article page