Table 4. Diffusivity equation—inverse modeling: PINN performance as function of noise.

This figure shows the average percentage errors of θ₁ and θ₂ for different numbers of training data, N_tr, as function of the noise levels. Here, the neural network architecture is kept fixed to 6 layers and 5 neurons per layer. The results are averages over 10 realizations.

Noise (ϵ)		0%	1%	5%	10%
Ntr
θ1	100	0.17	1.82	4.40	4.67
	250	0.15	0.30	1.00	1.98
	500	0.12	0.17	0.77	0.84
	1000	0.04	0.09	0.34	0.94
θ2	100	0.22	1.49	4.35	4.90
	250	0.24	0.52	1.80	2.45
	500	0.23	0.47	0.99	1.48
	1000	0.13	0.28	0.41	0.79