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Poster Communications 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-04081163 , version 1 (25-04-2023)

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  • HAL Id : hal-04081163 , version 1

Cite

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, May 2023, Kigali, Rwanda. . ⟨hal-04081163⟩

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