Operator Learning with Neural Fields: Tackling PDEs on General Geometries Supplemental Material Anonymous Author(s) Affiliation Address email

A.1 Initial Value Problem518 We use the datasets from Pfaff et al. (2021), and take the first and last frames of each trajectory as the519 input and output data for the initial value problem.520 Cylinder The dataset includes computational fluid dynamics (CFD) simulations of the flow around521 a cylinder, governed by the incompressible Navier-Stokes equation. These simulations were generated522 using COMSOL software, employing an irregular 2D-triangular mesh. The trajectory consists of 600523 timestamps, with a time interval of t =0 .01s between each timestamp.524 Airfoil The dataset contains CFD simulations of the flow around an airfoil, following the com-525 pressible Navier-Stokes equation. These simulations were conducted using SU2 software, using an526 irregular 2D-triangular mesh. The trajectory encompasses 600 timestamps, with a time interval of527 t =0 .008s between each timestamp.528 A.2 Dynamics Modeling529 2D-Navier-Stokes (Navier-Stokes) We consider the 2DNavier-Stokes equation as presented in Li530 et al. (2021); Yin et al. (2022).