Table 1
Identification of rheological parameters and pressure reconstruction accuracy. Each row corresponds to a test case with given reference values of the rheological parameters μs and μ2. The table reports the values identified by the PINN model, the corresponding relative errors Òμs and Òμ2 (in percent), and the relative L2 norm error Òp (in percent) on the reconstructed pressure field.
| μs | μ2 | Identified μs | Òμs (%) | Identified μ2 | εμ2 (%) | εp (%) |
|---|---|---|---|---|---|---|
| 0.2 | 0.32 | 0.203 | 1.39 | 0.297 | 7.07 | 2.71 |
| 0.2 | 0.44 | 0.203 | 1.26 | 0.425 | 3.35 | 2.85 |
| 0.3 | 0.42 | 0.304 | 1.39 | 0.390 | 7.03 | 3.06 |
| 0.3 | 0.54 | 0.304 | 1.45 | 0.516 | 4.42 | 2.89 |
| 0.4 | 0.52 | 0.403 | 0.86 | 0.498 | 4.29 | 2.75 |
| 0.4 | 0.64 | 0.405 | 1.24 | 0.610 | 4.62 | 2.96 |
| 0.5 | 0.62 | 0.502 | 0.44 | 0.612 | 1.30 | 4.14 |
| 0.5 | 0.74 | 0.504 | 0.79 | 0.724 | 2.13 | 3.79 |
| 0.6 | 0.72 | 0.601 | 0.13 | 0.734 | 1.94 | 8.43 |
| 0.6 | 0.84 | 0.604 | 0.64 | 0.832 | 1.00 | 7.32 |
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