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.

At a time when artificial intelligence algorithms are increasingly prevalent in our everyday lives (recruitment, customer relations, recommending content, banking and insurance, etc.), it is vital for Orange to ensure that the entire data value chain is managed responsibly and that potential discriminatory biases are identified and eliminated. The audit, carried out by Bureau Veritas, assessed Orange for its actions aimed at designing, developing and using inclusive artificial intelligence to promote diversity and avoid risks of discrimination before awarding the certification. The GEEIS-AI repository offers a way to raise awareness among the entire AI production chain, from design to operating the end product. In this way, a wide range of job lines and skills are at the service of the entire Orange ecosystem. This applies, in particular, to human resource management processes to guarantee they are not biased while encouraging diversity in AI job lines.