Table 1. Parameter estimation for all cases shown in Fig. 2.

We compare the estimated values ($\widehat{\mathbf{\theta }}$) and reference values (θ*) of unknown parameters. To calculate the relative error, we normalize the coordinates, the lengths and the modulus, and the tilting angle by the domain size (side length of the matrix), their respective reference values, and 180°, respectively. To improve the accuracy of case 5, we provide the PINN with additional displacement measurement points inside the solid and then retrain the PINN, which is shown in the table as “Case 5 (with internal data)”.

Case 0	$X_1^{(\mathrm{c})}$	$X_2^{(\mathrm{c})}$	A	B	Γ
Estimated value	0.0488	0.0987	0.3475	0.1582	−29.42°
Reference value	0.05	0.10	0.35	0.15	−30°
Absolute error (× 10−2, except Γ)	0.12	0.13	0.25	0.82	0.58°
Relative error (%)	0.12	0.13	0.71	5.47	0.32
Case 1	$X_1^{(\mathrm{c})}$	$X_2^{(\mathrm{c})}$	A	B	Γ
Estimated value	0.0479	0.0991	0.3440	0.1602	−29.02°
Reference value	0.05	0.10	0.35	0.15	−30°
Absolute error (× 10−2, except Γ)	0.21	0.09	0.60	1.02	0.98°
Relative error (%)	0.21	0.09	1.7	6.8	0.54
Case 2	$X_1^{(1)}$	$X_2^{(1)}$	$X_1^{(2)}$	$X_2^{(2)}$
Estimated value	−0.0399	0.3273	0.0396	−0.2315
Reference value	−0.0392	0.3474	0.0392	−0.2474
Absolute error (× 10−2)	0.07	2.01	0.04	1.59
Relative error (%)	0.07	2.01	0.04	1.59
Case 3	$X_1^{(\mathrm{c})}$	$X_2^{(\mathrm{c})}$	R
Estimated value	0.0506	0.0999	0.2525
Reference value	0.05	0.10	0.25
Absolute error (× 10−2)	0.06	0.01	0.25
Relative error (%)	0.06	0.01	1.00
Case 4	$X_1^{(1)}$	$X_2^{(1)}$	R (1)	$X_1^{(2)}$	$X_2^{(2)}$	R (2)
Estimated value	−0.15089	0.10018	0.20007	0.25045	−0.05008	0.15019
Reference value	−0.15	0.10	0.20	0.25	−0.05	0.15
Absolute error (× 10−2)	0.089	0.018	0.007	0.045	0.008	0.019
Relative error (%)	0.089	0.018	0.04	0.045	0.008	0.13
Case 5	$X_1^{(\mathrm{c})}$	$X_2^{(\mathrm{c})}$	R	μi
Estimated value	0.0496	0.0991	0.2583	0.0760
Reference value	0.05	0.10	0.25	0.0667
Absolute error (× 10−2)	0.04	0.09	0.83	0.93
Relative error (%)	0.04	0.09	3.3	13.9
Case 5 (with internal data)	$X_1^{(\mathrm{c})}$	$X_2^{(\mathrm{c})}$	R	μi
Estimated value	0.0495	0.0998	0.2524	0.0687
Reference value	0.05	0.10	0.25	0.0667
Absolute error (× 10−2)	0.05	0.02	0.24	0.20
Relative error (%)	0.05	0.02	0.96	3.0