Appendix A Illustrative Examples infinitesimal generator of the 2-dimensional rotation group, SO(2): v

By the prolongation formula, Eq. (4), the first prolongation in t is given by: ϕ As a final illustrative example of the symmetry criterion, we will follow Olver's example below: This choice was based on the previous research using PINN and DeepONets for solving Burgers' The output of the embedding vectors from both networks is 100 dimensional. For both the Heat equation and Burgers' equation experiments, we perform hyper-parameter tuning We also note that for Burgers' equation, we found that cosine similarity for L The results reported in Section 4 use cosine-similarity. We will make the data and the code available on GitHub. The corresponding mean-squared errors are reported in Table 2.