  Recently, Conditional Neural Fields (NeFs) have emerged as a powerful
modelling paradigm for PDEs, by learning solutions as flows in the latent space
of the Conditional NeF. Although benefiting from favourable properties of NeFs
such as grid-agnosticity and space-time-continuous dynamics modelling, this
approach limits the ability to impose known constraints of the PDE on the
solutions -- e.g. symmetries or boundary conditions -- in favour of modelling
flexibility. Instead, we propose a space-time continuous NeF-based solving
framework that - by preserving geometric information in the latent space -
respects known symmetries of the PDE. We show that modelling solutions as flows
of pointclouds over the group of interest $G$ improves generalization and
data-efficiency. We validated that our framework readily generalizes to unseen
spatial and temporal locations, as well as geometric transformations of the
initial conditions - where other NeF-based PDE forecasting methods fail - and
improve over baselines in a number of challenging geometries.
