Table 6. Biot’s equations—forward modeling: PINN performance as function of hyperparameters.

Sum of relative ${\mathcal{L}}^2$ errors between the exact and predicted values of u, v, and p for the validation set. The table shows the dependency on the different number of hidden layers, N_hl, and different number of neurons per layer, N_n. Here, the total number of training and collocation points is fixed to N_b = 96 and N_Π = 160, respectively.

Panel A: Average over 1 realization
Nn	2	5	10	20	40	80
Nhl
2	0.56506	0.01617	0.00782	0.00045	0.00021	0.00115
4	0.12080	0.00316	0.00013	0.00019	0.00020	0.00016
6	0.45949	0.02069	0.00052	0.00060	0.00010	0.00020
8	0.14333	0.00971	0.93757	0.00048	0.00034	0.00015
16	0.14052	0.14110	0.00041	0.00020	0.00020	0.00019
32	0.60485	0.03188	0.00866	0.00972	0.00028	0.00039
Panel B: Average over 3 realizations
Nn	2	5	10	20	40	80
Nhl
2	0.30761	0.01074	0.00346	0.00019	0.00026	0.00020
4	0.13684	0.01101	0.00032	0.00006	0.00007	0.00008
6	0.14338	0.04415	0.00018	0.00012	0.00009	0.00007
8	0.47702	0.01634	0.00020	0.00010	0.00008	0.00007
16	0.33020	0.13525	0.00081	0.00041	0.00013	0.00013
32	0.46854	0.61381	0.38437	0.07503	0.00087	0.00010
Panel C: Average over 27 realizations
Nn	2	5	10	20	40	80
Nhl
2	0.24203	0.02952	0.00180	0.00062	0.00021	0.00023
4	0.39596	0.06005	0.00368	0.00039	0.00010	0.00014
6	0.32610	0.07829	0.00018	0.00009	0.00010	0.00014
8	0.42070	0.12314	0.00037	0.00013	0.00010	0.00012
16	0.46364	0.12222	0.09613	0.05190	0.00012	0.00011
32	0.41372	0.38439	0.38473	0.03998	0.05080	0.01052