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Conference Papers Year : 2023

Continuous PDE Dynamics Forecasting with Implicit Neural Representations

Yuan Yin
Jean-Yves Franceschi
Alain Rakotomamonjy

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.
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Dates and versions

hal-03792179 , version 1 (29-09-2022)
hal-03792179 , version 2 (15-02-2023)

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Yuan Yin, Matthieu Kirchmeyer, Jean-Yves Franceschi, Alain Rakotomamonjy, Patrick Gallinari. Continuous PDE Dynamics Forecasting with Implicit Neural Representations. The Eleventh International Conference on Learning Representations, International Conference on Representation Learning, May 2023, Kigali, Rwanda. ⟨hal-03792179v2⟩

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