Continuous PDE Dynamics Forecasting with Implicit Neural Representations
Abstract
Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.
Cite
@article{arxiv.2209.14855,
title = {Continuous PDE Dynamics Forecasting with Implicit Neural Representations},
author = {Yuan Yin and Matthieu Kirchmeyer and Jean-Yves Franceschi and Alain Rakotomamonjy and Patrick Gallinari},
journal= {arXiv preprint arXiv:2209.14855},
year = {2023}
}