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

Advanced Modeling and Simulation in Engineering Sciences

Table 1 Regions for 5 variables function for various iterations

Iteration	Region	Maximum error between ANN function and Taylor polynomial
Initial	x₁ϵ [0.38,0.62], x₂ϵ [0.35,0.65], x₃ϵ [0.35,0.65], x₄ϵ [0.2,0.8], x₅ϵ [0.1,0.9]	0.3300
1st	x₁ϵ [0.44,0.56], x₂ϵ [0.425,0.575], x₃ϵ [0.425,0.575], x₄ϵ [0.35,0.65], x₅ϵ [0.25,0.75]	0.0170
2nd	x₁ϵ [0.47,0.53], x₂ϵ [0.4625,0.5375], x₃ϵ [0.4625,0.5375], x₄ϵ [0.425,0.575], x₅ϵ [0.375,0.625]	0.0022
3rd	x₁ϵ [0.455,0.545], x₂ϵ [0.44375,0.55625],x₃ϵ [0.44375,0.55625], x₄ϵ [0.3875,0.6125], x₅ϵ [0.3125,0.6875]	0.0081
4th	x₁ϵ [0.4475,0.5525], x₂ϵ [0.434375,0.565625], x₃ϵ [0.434375,0.565625], x₄ϵ [0.36875,0.63125], x₅ϵ [0.28125,0.71875]	0.0140
5th	x₁ϵ [0.45125,0.54875],x₂ϵ [0.4390625,0.5609375],x₃ϵ [0.4390625,0.5609375],x₄ϵ [0.378125,0.612875], x₅ϵ [0.296875,0.703125]	0.0120