Table 1 Summary of main information for each example.
From: Enhancing high-fidelity nonlinear solver with reduced order model
Example | 1 | 2.1 | 2.2 | 2.3 | 3 | 4 | |
|---|---|---|---|---|---|---|---|
Degrees of freedom | \(\left[ 128 \times 128\right]\) | 3993 | 3993 | 70602 | 2548 | 5823 | |
Parameters \(\varvec{\mu }\) | \(\varvec{\kappa }(x, y)\) | \(\nu , \mathrm {In_{D}}\) | \(\mathrm {In_{R}}, \mathrm {In_{D}}\) | x, y | \(t, \varvec{\kappa }_{\mathrm {top}}\) | \(t, \mathrm {F}\) | |
Training set (\(\mathrm {M_{train}}\)) | 9000 | 1600 | 1600 | 1600 | 13600 \((N_t \mathrm {M_{train}})\) | 4509 \((N_t \mathrm {M_{train}})\) | |
Validation set (\(\mathrm {M_{validation}}\)) | 500 | \(5\%\) of \(\mathrm {M_{train}}\) | \(5\%\) \(\mathrm {M_{train}}\) | \(5\%\) \(\mathrm {M_{train}}\) | \(5\%\) \(N_t \mathrm {M_{train}}\) | \(5\%\) \(N_t \mathrm {M_{train}}\) | |
Testing set (\(\mathrm {M_{test}}\)) | 500 | 100 | 100 | 100 | 1900 (\(N_t \mathrm {M_{test}}\)) | 1002 (\(N_t \mathrm {M_{test}}\)) | |
Training time (h) | cGAN-ROM | 4.00 | \(\times\) | \(\times\) | \(\times\) | \(\times\) | \(\times\) |
BT-ROM | \(\times\) | 0.67 | 0.67 | 1.0 | \(\times\) | \(\times\) | |
BBT-ROM | \(\times\) | 0.50 | 0.50 | 0.92 | 0.75 | 0.45 | |
in-ROM | \(\times\) | 1.00 | 1.00 | 1.83 | \(\times\) | \(\times\) | |
Number of nonlinear iterations (–) | Default init. | 15.04 | 6.10 | 6.30 | 6.16 | 934.68 | 6986.00 |
cGAN-ROM | 4.12 | \(\times\) | \(\times\) | \(\times\) | \(\times\) | \(\times\) | |
BT-ROM | \(\times\) | neg. | neg. | 5.40 | \(\times\) | \(\times\) | |
BBT-ROM | \(\times\) | 2.62 | 3.04 | 4.76 | 758.57 | 3412.00 | |
in-ROM | \(\times\) | 1.09 | 1.08 | neg. | \(\times\) | \(\times\) | |
Speed up (%) | cGAN-ROM | 72.63 | \(\times\) | \(\times\) | \(\times\) | \(\times\) | \(\times\) |
BT-ROM | \(\times\) | neg. | neg. | 12.33 | \(\times\) | \(\times\) | |
BBT-ROM | \(\times\) | 57.05 | 51.75 | 22.72 | 18.84 | 49.00 | |
in-ROM | \(\times\) | 82.12 | 82.86 | neg. | \(\times\) | \(\times\) | |
