GrINd: Grid Interpolation Network for Scattered Observations
This addresses the challenge of forecasting physical systems in scientific domains where data is sparse, extending deep learning applicability to real-world scenarios with limited data availability.
The paper tackles the problem of predicting spatiotemporal physical systems from sparse and scattered observational data by introducing GrINd, a network that maps observations to a grid and uses neural PDE models, achieving state-of-the-art performance on the DynaBench benchmark dataset.
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.