Table 6 Comparison of errors of various algorithm and transfer function for estimation of Rf.

From: Estimation and sensitivity analysis of fouling resistance in phosphoric acid/steam heat exchanger using artificial neural networks and regression methods

Algorithm

Transfer function

MSE training

MSE validation

MSE test

r2 training

r2 validation

r2 test

BFGS

Hyperbolic tangent sigmoid

1.668 × 10−11

2.585 × 10−11

1.707 × 10−11

0.995

0.993

0.995

Linear

4.221 × 10−10

3.374 × 10−10

4.595 × 10−10

0.864

0.911

0.865

Sigmoid

4.246 × 10−10

4.646 × 10−10

4.513 × 10−10

0.866

0.874

0.866

Gradient descent

Hyperbolic tangent sigmoid

6.833 × 10−11

5.966 × 10−11

5.209 × 10−11

0.982

0.986

0.986

Linear

1.036 × 10−09

7.187 × 10−10

1.186 × 10−09

0.786

0.911

0.735

Sigmoid

4.400 × 10−10

4.563 × 10−10

4.798 × 10−10

0.863

0.879

0.862

Conjugate gradient

Hyperbolic tangent sigmoid

4.052 × 10−11

5.628 × 10−11

4.422 × 10−11

0.988

0.986

0.990

Linear

4.478 × 10−10

3.271 × 10−10

4.681 × 10−10

0.859

0.914

0.862

Sigmoid

4.349 × 10−10

4.625 × 10−10

4.545 × 10−10

0.864

0.876

0.865