# GrINd: Grid Interpolation Network for Scattered Observations

arXiv: https://arxiv.org/abs/2403.19570 · HTML: https://mlsanity.com/paper/2403.19570/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 52 references that are in the map.
- First posted on arXiv 28 Mar 2024.

## Builds on (most cited first, 27 of 27)

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- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
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- [Learning Dynamical Systems from Partial Observations](https://mlsanity.com/paper/1902.11136/) (2019)
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- [cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs](https://mlsanity.com/paper/2102.08463/) (2021)
- [NeuralPDE: Modelling Dynamical Systems from Data](https://mlsanity.com/paper/2111.07671/) (2021)
- [DynaBench: A benchmark dataset for learning dynamical systems from low-resolution data](https://mlsanity.com/paper/2306.05805/) (2023)
- [Towards Causal Representations of Climate Model Data](https://mlsanity.com/paper/2312.02858/) (2023)
- [PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Network](https://mlsanity.com/paper/2208.04319/) (2022)

## Abstract (arXiv)

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.