Table 10 Statistical metrics for the training, testing, and forecasting performance of the model (3) for pH, TDS, EC, and Na\(^+\).

From: Evaluating physics informed neural networks for water contamination risk prediction and environmental sustainability

Parameter

Statistical Measures

\(\textrm{G}_{1}\)

\(\textrm{G}_{2}\)

\(\textrm{G}_{3}\)

\(\textrm{G}_{4}\)

pH

\(\textrm{R}^{2}\) Train

0.980

0.984

0.981

0.991

\(\textrm{R}^{2}\) Test

0.957

0.954

0.960

0.954

\(\textrm{R}^{2}\) Forecast

0.961

0.966

0.958

0.947

MSE

0.049

0.023

0.027

0.042

TDS

\(\textrm{R}^{2}\) Train

0.980

0.984

0.983

0.980

\(\textrm{R}^{2}\) Test

0.958

0.969

0.963

0.953

\(\textrm{R}^{2}\) Forecast

0.946

0.964

0.948

0.944

MSE

0.044

0.045

0.012

0.054

EC

\(\textrm{R}^{2}\) Train

0.988

0.981

0.983

0.981

\(\textrm{R}^{2}\) Test

0.966

0.958

0.950

0.955

\(\textrm{R}^{2}\) Forecast

0.951

0.952

0.947

0.948

MSE

0.016

0.018

0.027

0.079

Na\(^+\)

\(\textrm{R}^{2}\) Train

0.985

0.983

0.987

0.986

\(\textrm{R}^{2}\) Test

0.965

0.952

0.967

0.955

\(\textrm{R}^{2}\) Forecast

0.960

0.957

0.949

0.948

MSE

0.032

0.066

0.024

0.014