Operator Learning with Neural Fields: Tackling PDEs on General Geometries Supplemental Material Anonymous Author(s) Affiliation Address email A Dataset Details 517 A.1 Initial Value Problem

We use the datasets from Pfaff et al. ( 2021), and take the first and last frames of each trajectory as the By sampling initial conditions as in Li et al. ( 2021), we generated different trajectories on a In total, we collected 256 trajectories for training, and 16 for evaluation. We created 16 trajectories for the training set and 2 trajectories for the test set. Each long trajectory is then sliced into sub-trajectories of 40 timestamps each. As a result, the training set contains 64 trajectories, while the test set contains 8 trajectories. We use the datasets provided by Li et al. ( 2022a) and adopt the original authors' train/test split for The viscous effect is ignored. The initial NACA-0012 shape is mapped onto a "cubic" design element with 8 control The data was generated with a finite element solver with about 100 quadratic quadrilateral elements.