  Predicting the evolution of spatiotemporal physical systems from sparse and
scattered observational data poses a significant challenge in various
scientific domains. Traditional methods rely on dense grid-structured data,
limiting their applicability in scenarios with sparse observations. To address
this challenge, we introduce GrINd (Grid Interpolation Network for Scattered
Observations), a novel network architecture that leverages the high-performance
of grid-based models by mapping scattered observations onto a high-resolution
grid using a Fourier Interpolation Layer. In the high-resolution space, a
NeuralPDE-class model predicts the system's state at future timepoints using
differentiable ODE solvers and fully convolutional neural networks
parametrizing the system's dynamics. We empirically evaluate GrINd on the
DynaBench benchmark dataset, comprising six different physical systems observed
at scattered locations, demonstrating its state-of-the-art performance compared
to existing models. GrINd offers a promising approach for forecasting physical
systems from sparse, scattered observational data, extending the applicability
of deep learning methods to real-world scenarios with limited data
availability.
