Speaker
Description
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--such as 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 of the Conditional NeF-preserves known symmetries of the PDE. We show that modelling solutions as flows of pointclouds over the group of interest improves generalization and data-efficiency. Furthermore, we validate 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.