Table 11 Performance comparison of the predictive solution and predictive parameter of Eq. (47).

From: Data-driven solutions and parameter estimations of a family of higher-order KdV equations based on physics informed neural networks

Case

PINN(\(\tanh\))

PINN(\(\sin\)e)

Loss

4.3772 × 10−4

1.8681 × 10−5

\(\mathbb {L}_{2}\) Error u

1.6164 × 10−3

4.1269 × 10−4

Error \(\alpha\)

0.0766%

0.0117%

Error \(\beta\)

0.1217%

0.0106%

\(\alpha\)

0.9992

0.9998

\(\beta\)

0.9987

0.9998

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