Figure 4 | Scientific Reports

Figure 4

From: Affine transformations accelerate the training of physics-informed neural networks of a one-dimensional consolidation problem

Figure 4

Field plots for a replicate run with the best values from a Bayes optimization in terms of relative \({\mathscr {L}}_2\) error (\(w_u=3.18\textrm{e}{-}3\), \(w_b=1.26\textrm{e}{-}2\), \(b_u=9.86\textrm{e}{-}5\), and \(b_p=3.82\textrm{e}{-}4\)). Analytically calculated pressure and displacement curves, the AfPINN solution, and the absolute difference between the exact (displacement u and pressure p) and AfPINN (displacement \(\hat{u}\) and pressure \(\hat{p}\)) solutions are plotted. The values were evaluated on a grid of \(101 \times 101\) points resulting in an \({\mathscr {L}}_2\) relative error of \(7.50\textrm{e}{-}3\).

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