Theory and Modern Applications
Table 1 Absolute and mean squared errors between the reported infection data and infection rate outputs of the PINN with training data covering the calendar weeks 10 in 2020 through 52 in 2021, or the NSFD scheme, if distinct weighting or transmission risk parameter values are used
From: A physics-informed neural network to model COVID-19 infection and hospitalization scenarios
size of α in PINN | diff (regularized by 10−6) | \(\mathrm{MSE}_{\mathrm{diff}}\) (regularized by 10−11) |
|---|---|---|
0.3 | 6.5338 | 0.64343 |
0.5 | 5.3861 | 0.57782 |
0.65 | 4.6681 | 0.53966 |
0.9 | 3.4886 | 0.48237 |
0.93 | 3.4015 | 0.47992 |
0.945 | 3.3726 | 0.47811 |
0.9475 | 3.3601 | 0.47772 |
0.95 | 3.3551 | 0.47601 |
0.9525 | 3.3599 | 0.47746 |
0.955 | 3.3717 | 0.47799 |
0.96 | 3.4683 | 0.48099 |
0.97 | 3.5714 | 0.48289 |
0.98 | 3.7614 | 0.49263 |
0.99 | 3.9904 | 0.49852 |
size of β in NSFD | diff (regularized by 10−6) | \(\mathrm{MSE}_{\mathrm{diff}}\) (regularized by 10−11) |
|---|---|---|
1.95⋅10−9 | 5.7471 | 0.71234 |
1.98⋅10−9 | 4.8266 | 0.50868 |
2.00⋅10−9 | 5.2971 | 0.62172 |
2.04⋅10−9 | 8.9822 | 1.58271 |
2.08⋅10−9 | 13.8549 | 2.63107 |
2.12⋅10−9 | 18.8948 | 6.80091 |