In this talk, I hope to initiate some discussions on a few tentative ideas of engaging machine learning techniques in traditionally PDE-based application tasks. Two application configurations will be considered. One involves repetitive PDE simulations for various parameter realizations. Such simulations may need to be performed quickly in real time, which may inspire an offline-online strategy. The other application configuration arises from the classical PDE-constrained optimization problem, where feature engineering can be difficult, yet crucial. Finally, the issue of parameter sampling in generating training data with PDE models will be touched upon.
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