Table 3 The MAE and RMSE for the four experiments. Errors, in terms of RMSE and MAE, of the PINN provided solution with respect to numerical solution of bidimensional Gray-Scott system. Experiments are conducted for different configurations of the parameter couple (F,K) which give four types of Turing patterns during the temporal evolution
From: Physics-informed neural networks approach for 1D and 2D Gray-Scott systems
\({\varvec{PATTERNS}}\) | \({\varvec{MAE}}_{{\varvec{u}}}\) | \({\varvec{MAE}}_{{\varvec{v}}}\) | \({\varvec{RMSE}}_{{\varvec{u}}}\) | \({\varvec{RMSE}}_{{\varvec{v}}}\) |
|---|---|---|---|---|
FLOWER | 0.22 | 0.10 | 0.30 | 0.16 |
MITOSIS | 0.19 | 0.07 | 0.26 | 0.11 |
SOLITON | 0.22 | 0.09 | 0.29 | 0.13 |
ZEBRAFISH | 0.23 | 0.10 | 0.29 | 0.14 |