GrINd: Grid Interpolation Network for Scattered Observations

• URL: http://arxiv.org/abs/2403.19570v1
• Date: Thu, 28 Mar 2024 16:52:47 GMT
• Title: GrINd: Grid Interpolation Network for Scattered Observations
• Authors: Andrzej Dulny, Paul Heinisch, Andreas Hotho, Anna Krause,
• Abstract summary: We introduce GrINd (Grid Interpolation for Scattered Observations), a novel network architecture that maps scattered observations onto a high-resolution grid. 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. We empirically evaluate GrINd on theBench Dyna benchmark dataset, comprising six different physical systems observed at scattered locations.
• Score: 3.1516690022588616
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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