|
|
|
A physics-constrained deep residual network for solving the sine-Gordon equation
|
|
Jun Li(李军),Yong Chen(陈勇)
|
|
| |
Table 2. Relative ${{\mathbb{L}}}_{2}$ errors for different numbers of data points under the distortion of different noise levels.
|
|
| Noise | 0% | | | | Noise | 1% | | | |
|---|
| Nf | Nf |
|---|
| Nu | 1000 | 5000 | 10 000 | 20 000 | Nu | 1000 | 5000 | 10 000 | 20 000 |
|---|
| 10 | 3.67e-01 | 1.47e-01 | 1.02e-01 | 2.27e-01 | 10 | 5.17e-01 | 1.41e-01 | 8.58e-02 | 5.34e-02 | | 50 | 6.98e-03 | 2.12e-03 | 1.14e-03 | 1.68e-03 | 50 | 1.35e-02 | 5.71e-03 | 5.81e-03 | 3.75e-03 | | 100 | 2.91e-03 | 1.48e-03 | 1.37e-03 | 1.23e-03 | 100 | 9.52e-03 | 5.95e-03 | 6.92e-03 | 3.55e-03 | | 200 | 1.07e-03 | 1.21e-03 | 9.73e-04 | 6.09e-04 | 200 | 3.60e-03 | 1.42e-03 | 2.59e-03 | 2.03e-03 |
|
|
|