Appendix 387 A Illustrative Examples

By the prolongation formula, Eq. (4), the first prolongation in t is given by: As a final illustrative example of the symmetry criterion, we will follow Olver's example below: 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 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.