Table 4 Results of Algorithm 1 with gaussian noise added to sparse data for Allen–Cahn equation.
From: Parameter identification for PDEs using sparse interior data and a recurrent neural network
GaussiaNoise | ||||
|---|---|---|---|---|
Results | \(\sigma = 0.01\) | \(\sigma = 0.03\) | \(\sigma = 0.05\) | \(\sigma = 0.1\) |
Relative \(L_{2}\) errors | 3.64e\(-\)3 | 8.09e\(-\)3 | 9.91e\(-\)2 | 1.64e\(-\)2 |
Estimated diffusion rate error | 1.67e\(-\)1 | 3.94e\(-\)1 | 4.41e\(-\)1 | 5.62e\(-\)1 |
Estimated reaction coefficient error | 6.11e\(-\)3 | 9.02e\(-\)3 | 1.13e\(-\)2 | 2.93\(-\)2 |
