Continuous PDE Dynamics Forecasting with Implicit Neural Representations

Understand

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.