Appendixes A An Example for Scenario 2 We give an example of G(A)

Below is a detailed explanation of the comparative methods covered in the paper. The network architecture of PI-DeepONet used for Burgers' equation is such that both In order to solve the Eq. Fig.6 shows model predictions of MAD-L and MAD-LM compared with the reference solutions under Fig.7(a) shows that the accuracy of MAD-L after convergence increases with Fig.7(b) shows that the accuracy and convergence speed of MAD-LM do not change For Burgers' equation, we also consider the scenario when the viscosity coefficients Fig.8 compares the convergence curves of mean MAD-LM has obvious speed and accuracy improvement over From-Scratch and Transfer-Learning . We investigated the effect of the dimension of the latent vector (latent size) in Burgers' equation on performance. As can be seen from Fig.9(a), for MAD-L, different latent sizes have different performances and the best performance is achieved when it is equal to 128.