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Continuous PDE Dynamics Forecasting with Implicit Neural Representations
Yuan Yin · Matthieu Kirchmeyer · Jean-Yves Franceschi · Alain Rakotomamonjy · Patrick Gallinari

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in AI for Science: Progress and Promises »
Event URL: https://openreview.net/forum?id=iB3KkHR4gc »

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.

Keywords: Dynamical Systems · Implicit neural representations · generalization · PDEs · physics · partial differential equations · continuous models · spatiotemporal forecasting · INRs

Author Information

Yuan Yin (Sorbonne Université, ISIR)
Matthieu Kirchmeyer (Sorbonne Université & Criteo)
Jean-Yves Franceschi (Criteo AI Lab)
Alain Rakotomamonjy (Université de Rouen Normandie Criteo AI Lab)
Patrick Gallinari (Sorbonne Universite, Criteo AI Lab)

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