Fig. 5: Testing the local solution operator on diverse testing functions.
From: One-shot learning for solution operators of partial differential equations
a A phase-shifted sine wave, \(f=\sin (2\pi x+\pi )\). b A cosine wave, \(f=\cos (2\pi x)\). c A higher-frequency sine wave, \(f=\sin (3\pi x)\). d A sine wave with very high frequency, \(f=2\sin (9\pi x)\). e A sum of two sine waves at moderate and high frequencies, \(f=\sin (6\pi x)+\sin (14\pi x)\). f A sum of multiple weighted sine waves at different frequencies, \(f=0.8\sin (6\pi x)+0.6\sin (14\pi x)+0.4\sin (26\pi x)+0.2\sin (42\pi x)\). The first column is various new f; the second column is the corresponding ground truth u; the third column is the FPI prediction for each f; and the last column is the absolute error between the ground truth u and the prediction.
