Continuous PDE Dynamics Forecasting with Implicit Neural Representations
This addresses limitations in real-world applications like weather prediction by allowing flexible extrapolation from sparse or irregular data, though it is incremental in combining existing techniques for a known bottleneck.
The paper tackles the problem of forecasting PDE dynamics with flexible spatiotemporal discretization by introducing DINo, a data-driven model that uses Implicit Neural Representations and learned ODEs to enable extrapolation at arbitrary locations and outperforms alternative neural methods in generalization scenarios.
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.