Fig. 6: Prediction comparison by iterations.
From: Automatic network structure discovery of physics informed neural networks via knowledge distillation
a, d, PINN predictions; b, e, PINN-post predictions; c and f, Ψ-NN predictions. The optimization tendency of different models. In the figures of the first row, the red dashed line represents the true value of u as x2 varies when x1 = 0.8. Each green-blue gradient curve represents the network output at training steps from 1000 to 5000, with an interval of 300. In the second row of figures, the results at several training steps are plotted on a two-dimensional coordinate plane to illustrate the symmetry breaking in PINN during the iterative process, as well as the symmetry preservation in PINN-post and Ψ-NN.
