# Towards High Resolution Probabilistic Coastal Inundation Forecasting from Sparse Observations

arXiv: https://arxiv.org/abs/2505.05381 · HTML: https://mlsanity.com/paper/2505.05381/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 54 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 19 of 19)

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- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [Scalable Spatiotemporal Prediction with Bayesian Neural Fields](https://mlsanity.com/paper/2403.07657/) (2024)
- [Learning Non-Stationary Space-Time Models for Environmental Monitoring](https://mlsanity.com/paper/1804.10535/) (2018)

## Abstract (arXiv)

Coastal flooding poses increasing threats to communities worldwide, necessitating accurate and hyper-local inundation forecasting for effective emergency response. However, real-world deployment of forecasting systems is often constrained by sparse sensor networks, where only a limited subset of locations may have sensors due to budget constraints. To approach this challenge, we present DIFF -SPARSE, a masked conditional diffusion model designed for probabilistic coastal inundation forecasting from sparse sensor observations. DIFF -SPARSE primarily utilizes the inundation history of a location and its neighboring locations from a context time window as spatiotemporal context. The fundamental challenge of spatiotemporal prediction based on sparse observations in the context window is addressed by introducing a novel masking strategy during training. Digital elevation data and temporal co-variates are utilized as additional spatial and temporal contexts, respectively. A convolutional neural network and a conditional UNet architecture with cross-attention mechanism are employed to capture the spatiotemporal dynamics in the data. We trained and tested DIFF -SPARSE on coastal inundation data from the Eastern Shore of Virginia and systematically assessed the performance of DIFF -SPARSE across different sparsity levels 0%, 50%, 95% missing observations. Our experiment results show that DIFF -SPARSE achieves upto 62% improvement in terms of two forecasting performance metrics compared to existing methods, at 95% sparsity level. Moreover, our ablation studies reveal that digital elevation data becomes more useful at high sparsity levels compared to temporal co-variates.