# Physics-Aware Downsampling with Deep Learning for Scalable Flood Modeling

arXiv: https://arxiv.org/abs/2106.07218 · HTML: https://mlsanity.com/paper/2106.07218/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 14 Jun 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017)
- [Learning to Optimize Multigrid PDE Solvers](https://mlsanity.com/paper/1902.10248/) (2019)
- [Comparing recurrent and convolutional neural networks for predicting wave propagation](https://mlsanity.com/paper/2002.08981/) (2020)
- [Divide-and-Conquer Checkpointing for Arbitrary Programs with No User Annotation](https://mlsanity.com/paper/1708.06799/) (2017)
- [Inundation Modeling in Data Scarce Regions](https://mlsanity.com/paper/1910.05006/) (2019)

## Built on by (most cited first, 4 of 4)

- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networks](https://mlsanity.com/paper/2402.08367/) (2024)
- [MODS: Multi-source Observations Conditional Diffusion Model for Meteorological State Downscaling](https://mlsanity.com/paper/2506.14798/) (2025)
- [Feature Mapping in Physics-Informed Neural Networks (PINNs)](https://mlsanity.com/paper/2402.06955/) (2024)

## Abstract (arXiv)

Background: Floods are the most common natural disaster in the world, affecting the lives of hundreds of millions. Flood forecasting is therefore a vitally important endeavor, typically achieved using physical water flow simulations, which rely on accurate terrain elevation maps. However, such simulations, based on solving partial differential equations, are computationally prohibitive on a large scale. This scalability issue is commonly alleviated using a coarse grid representation of the elevation map, though this representation may distort crucial terrain details, leading to significant inaccuracies in the simulation. Contributions: We train a deep neural network to perform physics-informed downsampling of the terrain map: we optimize the coarse grid representation of the terrain maps, so that the flood prediction will match the fine grid solution. For the learning process to succeed, we configure a dataset specifically for this task. We demonstrate that with this method, it is possible to achieve a significant reduction in computational cost, while maintaining an accurate solution. A reference implementation accompanies the paper as well as documentation and code for dataset reproduction.