# Learned Response-Field Inertia Operator for HEC-RAS 2D Water-Surface Elevation Prediction

arXiv: https://arxiv.org/abs/2606.06385 · HTML: https://mlsanity.com/paper/2606.06385/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [A greedy non-intrusive reduced order model for shallow water equations](https://mlsanity.com/paper/2002.11329/) (2020)
- [Rapid Flood Inundation Forecast Using Fourier Neural Operator](https://mlsanity.com/paper/2307.16090/) (2023)
- [Deep Vision-Based Framework for Coastal Flood Prediction Under Climate Change Impacts and Shoreline Adaptations](https://mlsanity.com/paper/2406.15451/) (2024)
- [Accelerating HEC-RAS: A Recurrent Neural Operator for Rapid River Forecasting](https://mlsanity.com/paper/2507.15614/) (2025)
- [Deep Learning Hydrodynamic Forecasting for Flooded Region Assessment in Near-Real-Time (DL Hydro-FRAN)](https://mlsanity.com/paper/2305.12052/) (2023)

## Built on by (most cited first, 1 of 1)

- [Knowledge-Graph-Augmented Chronos-2 for HEC-RAS Surrogate Forecasting](https://mlsanity.com/paper/2609.21381/) (2026)

## Abstract (arXiv)

This article presents a cross-dataset evaluation of learned native-cell surrogate models for solver-consistent water-surface elevation (WSE) prediction in HEC-RAS 2D. To avoid raster remapping error and information-access confounding, surrogates are evaluated directly on the original nonuniform computational cells under an explicit policy that separates static project inputs, current hydraulic state, project-input forcing, calibration-derived quantities, and future solver-output targets. We introduce the Learned Response-Field Inertia Operator (LRFIO), a no-forcing, increment-based learned surrogate that calibrates an inertial response operator from solved HEC-RAS trajectories and deploys the retained operator through closed-form native-cell rollout. LRFIO evaluates a base-case-first response hierarchy consisting of persistence, global calibrated inertia, and segmented response-field inertia. Segmentation, residual correction, and neuralized inertia are treated as learnable modeling choices, with added complexity retained only when validation evidence justifies its cost. Evaluated across four diverse HEC-RAS 2D benchmarks, LRFIO retains different response structures for different domains, demonstrating adaptive learned complexity. The selector audit shows controlled complexity with a maximum validation regret of 4.30%. During deployment, retained rollout times range from 0.003 s to 0.242 s, and the Beaver Bayou measured-solve comparison gives an estimated 2.75 x 10^4 horizon-normalized speedup over HEC-RAS. These results indicate that the current native-cell increment is a strong solver-conditioned predictive scaffold and that added response-field, neural, or spatial complexity should be retained only when empirically justified.