A Geometry-Informed Neural Operator surrogate of LISFLOOD-FP for rapid pluvial-fluvial flood forecasting: the case of Forlì, Italy

Samuele Maria Garofalo; Fabio Limardo; Simonetta Bodojra; Mohammad Amin Nabian; Mehdi Taghizadeh

cs.LGNov 2, 2026

A Geometry-Informed Neural Operator surrogate of LISFLOOD-FP for rapid pluvial-fluvial flood forecasting: the case of Forlì, Italy

Authors: Samuele Maria Garofalo, Fabio Limardo, Simonetta Bodojra, Mohammad Amin Nabian, Mehdi Taghizadeh

Organizations: Data Reply, Turin, Italy · NVIDIA, Santa Clara, CA, USA · University of Virginia, USA

Abstract

Physically based two-dimensional hydraulic models are too slow for real-time inundation forecasting and large ensembles. We present a time-dependent geometry-informed neural operator (GINO) surrogate of LISFLOOD-FP for the municipality of Forlì (Italy), severely affected by the May 2023 Emilia-Romagna floods. The surrogate is designed for an operational setting in which only river stage gauges and rain gauges are available. A reproducible pipeline turns public regional observations into a physically based training set: each river inflow is driven by the first stage gauge downstream of it through a calibrated water-surface boundary condition, and rain enters as SCS-CN effective rainfall. The surrogate is an autoregressive GINO trained on 216 simulations of 24 observed events with scaled forcing. It predicts volume-conserving polygon-mean depths on an exposure-based Voronoi mesh of 659 nodes, with a 20 min step over 72 h. The surrogate is tested on 38 independent observed events that it never saw during training. On these events it reaches a critical success index (CSI) of 0.934 at 0.05m and 0.844 at 0.3 m, a depth RMSE of 0.008m and an $R^2$ of 0.984 for maximum-depth maps. On one NVIDIA A10G GPU a 72-h forecast takes 1.7 s instead of 55 s with LISFLOOD-FP, and a 50-member ensemble, computed in a single batched rollout, takes 6.2 s instead of about 46 min, which makes probabilistic flood forecasting practical. These results show that neural-operator surrogates can deliver accurate pluvial-fluvial flood forecasts driven by river stage for operational early warning.

Figures & tables

Figure 1: Study area: LISFLOOD-FP domain on the conditioned DEM, with the municipality of Forlì (dashed; extent of the GINO mesh, $228.36\text{\,}\mathrm{k}\mathrm{m}^{2}$ ), the Montone, Rabbi and Bidente–Ronco rivers, the three river inflow cells (stars), the ARPAE stage gauges (red: driver gauges of the three inflows), the 19 rain gauges inside the rain box (dotted) and, shaded, the areas flooded on 16–17 May 2023 ( Regione Emilia-Romagna – Agenzia regionale per la sicurezza territoriale e la protezione civile, 2025 ) . Inset: location in Italy, with Emilia-Romagna in blue.

Figure 2: Overview of the workflow, illustrated with the 16 May 2023 event. (a) Observed stage at the three driver gauges and domain-mean rain (bars, inverted axis), which define the stage boundary conditions and the effective rain. (b) LISFLOOD-FP maximum water depth on the $100\text{\,}\mathrm{m}$ grid. (c) Polygon-mean maximum depth on the 659-node Voronoi mesh, the training target of the surrogate. (d) Time-dependent GINO, applied autoregressively. (e) Ensemble forcing: 50 perturbed Montone stage series (grey) around the observed one (black), propagated by the surrogate in a single batched rollout.

Figure 3: Exposure-based Voronoi mesh of the municipality of Forlì (659 polygons; median area $25\text{\,}\mathrm{h}\mathrm{a}$ ), with the main rivers.

Figure 4: Architecture of the time-dependent GINO surrogate. The node features on the Voronoi mesh are encoded onto a regular $32\times 32$ latent grid by a GNO, processed globally by four Fourier layers and decoded back to the nodes by a second GNO, which predicts the depth increment of Eq. ( 3 ); the new depth is fed back as input for the next $20\text{\,}\mathrm{m}\mathrm{i}\mathrm{n}$ step.

Channel	Description
Static
Elevation	Polygon mean of the conditioned DEM (m)
Slope	Polygon mean of the terrain slope
Curvature	Polygon mean of the terrain curvature
Manning	Polygon mean of Manning’s $n$
Area	Polygon area

Table 1: Input channels of the GINO surrogate (per node and time step).

Parameter	Value
Input / output channels	12 / 1 (depth increment)
GNO radius (encoder, decoder)	0.15 (normalised coordinates)
Latent grid	$32\times 32$
FNO modes	$16\times 16$
FNO layers / hidden channels	4 / 64 (GELU)
GNO kernel MLPs (encoder; decoder)	$[80,80,80]$ ; $[512,256]$ , linear transform

Table 2: Hyper-parameters of the GINO surrogate and of its training.

Figure 5: LISFLOOD-FP maximum water depth above $0.10\text{\,}\mathrm{m}$ over $72\text{\,}\mathrm{h}$ for the 16 May 2023 event compared, cell by cell, with the regional perimeter of the areas flooded on 16–17 May 2023 ( Regione Emilia-Romagna – Agenzia regionale per la sicurezza territoriale e la protezione civile, 2025 ) , municipality of Forlì.

Figure 6: Water depth simulated by LISFLOOD-FP for the 16 May 2023 event, from $12\text{\,}\mathrm{h}$ to $72\text{\,}\mathrm{h}$ after the start of the simulation window.

Figure 7: Maximum water depth simulated by LISFLOOD-FP over $72\text{\,}\mathrm{h}$ for a selection of runs of the final set-up, ordered from the most to the least flooded.

Metric	Validation ( $n=22$ )	Test ( $n=38$ )
RMSE (m)	$0.006\pm 0.007$	$0.008\pm 0.009$
CSI ( $0.05\text{\,}\mathrm{m}$ )	$0.936\pm 0.045$	$0.934\pm 0.039$
CSI ( $0.3\text{\,}\mathrm{m}$ )	$0.901\pm 0.081$	$0.844\pm 0.084$
RMSE, area-weighted (m)	$0.007\pm 0.008$	$0.009\pm 0.010$
CSI ( $0.05\text{\,}\mathrm{m}$ ), area-weighted	$0.942\pm 0.039$	$0.936\pm 0.027$
CSI ( $0.3\text{\,}\mathrm{m}$ ), area-weighted	$0.899\pm 0.079$	$0.836\pm 0.089$

Table 3: Accuracy of the GINO surrogate on the 22 validation simulations and on the 38 independent test events, mean

\pm

standard deviation over simulations.

Figure 8: Flood volume (sum over nodes of the depth anomaly times the polygon area, $\mathrm{m}^{3}$ ) for all 38 test events: LISFLOOD-FP (left) and free-running GINO surrogate rollout over $72\text{\,}\mathrm{h}$ (right). Line colour: total effective rainfall of the event (mm).

Figure 9: Error as a function of lead time, median over the 38 test events in $6\text{\,}\mathrm{h}$ bins: (left) volume error relative to the true peak volume; (centre) area-weighted CSI; (right) MAE on nodes wet in truth or prediction (m). Node-level flood metrics on the anomaly above each node’s base level.

Figure 10: Two test events of different magnitude: 2016-03-18 (top) and 2006-03-05 (bottom). Left: wet fraction of the municipality (% of the area with anomaly above $5\text{\,}\mathrm{c}\mathrm{m}$ ); centre: flood volume (sum of anomaly times area, $\mathrm{m}^{3}$ ); right: depth anomaly at the node with the largest anomaly, with domain-mean rainfall (grey bars, right axis). Solid blue: LISFLOOD-FP; dashed red: GINO surrogate (free-running rollout, $72\text{\,}\mathrm{h}$ ).

Figure 11: Node depth anomaly (m) at the time of the true volume peak ( $34.7\text{\,}\mathrm{h}$ ) for the test event 2006-03-05: LISFLOOD-FP (left), GINO surrogate (centre) and error, prediction minus truth (right; red = overestimation, blue = underestimation). Each dot is a node of the 659-node Voronoi mesh; coordinates in UTM 32N (m).

Figure 12: 50-member ensemble forecast with the GINO surrogate for a test event, at the time of the true volume peak. Top: LISFLOOD-FP depth anomaly (m), ensemble-mean anomaly (m) and probability of an anomaly above $0.10\text{\,}\mathrm{m}$ (%). Bottom: ensemble spread (standard deviation, m); histogram of the flood probability over the evaluated nodes; perturbed boundary water surface elevation of the 50 members (grey) and observed boundary condition (red) at the node with the largest stage range, with the time of the true peak (dotted line).

Geometry-Aware Neural Operators

See all 8 papers

Toward an Operational GNN-Based Multimesh Surrogate for Fast Flood Forecasting
Apr 3, 2026Valentin Mercier, Serge Gratton, Lapeyre Corentin +1Flood Forecasting Neural Surrogate Modeling
Toulouse INP, IRIT, EPE UT · Université de Toulouse, INP, IRIT, Toulouse, France · IRIT, EPE UT, Toulouse INP +3
Physics-Informed CNN-LSTM for Street-Scale Urban Flood Prediction: Reconciling Aggregate Accuracy and Street-Level Plausibility
Jul 27, 2026Luc DCosta, Yidi Wang, Jonathan L. Goodall +1Convolutional RNNs Flood Inundation Mapping
Chandra Robot Autonomy Lab, Department of Computer Science, University of Virginia, Charlottesville, VA 22904, USA · Link Lab, Multidisciplinary Research Center, University of Virginia, Charlottesville, VA 22904, USA · Hydroinformatics Research Group, Department of Civil and Environmental Engineering, University of Virginia, Charlottesville, VA 22904, USA
Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations
May 13, 2026Phillip Si, Yuan Qiu, Omar Sallam +4Digital Twins PDE Surrogate Modeling
School of Computational Science and Engineering, Georgia Institute of Technology, 756 West Peachtree Street Northwest, Atlanta, 30308, GA, USA · Environmental Science Division, Argonne National Laboratory, 9700 S Cass Ave, Lemont, 60439, IL, USA

Apr 3, 2026J/K move · Enter open · S save

Toward an Operational GNN-Based Multimesh Surrogate for Fast Flood Forecasting

Valentin Mercier, Serge Gratton, Lapeyre Corentin, Gwenaël Chevallet

Toulouse INP, IRIT, EPE UT · Université de Toulouse, INP, IRIT, Toulouse, France · IRIT, EPE UT, Toulouse INP+3

Flood Forecasting Neural Surrogate Modeling PDE Surrogate Modeling Flood Inundation Mapping Spatiotemporal GNNs

Open paper AskPDF arXiv

Operational flood forecasting still relies on high-fidelity two-dimensional hydraulic solvers, but their runtime can be prohibitive for rapid decision support on large urban floodplains. In parallel, AI-based surrogate models have shown strong potential in several areas of computational physics for accelerating otherwise expensive high-fidelity simulations. We address this issue on the lower Têt River (France), starting from a production-grade Telemac2D model defined on a high-resolution unstructured finite-element mesh with more than

4\times 10^5

nodes. From this setup, we build a learning-ready database of synthetic but operationally grounded flood events covering several representative hydrograph families and peak discharges. On top of this database, we develop a graph-neural surrogate based on projected meshes and multimesh connectivity. The projected-mesh strategy keeps training tractable while preserving high-fidelity supervision from the original Telemac simulations, and the multimesh construction enlarges the effective spatial receptive field without increasing network depth. We further study the effect of an explicit discharge feature

Q(t)

and of pushforward training for long autoregressive rollouts. The experiments show that conditioning on

Q(t)

is essential in this boundary-driven setting, that multimesh connectivity brings additional gains once the model is properly conditioned, and that pushforward further improves rollout stability. Among the tested configurations, the combination of

Q(t)

, multimesh connectivity, and pushforward provides the best overall results. These gains are observed both on hydraulic variables over the surrogate mesh and on inundation maps interpolated onto a common

25\,\mathrm{m}

regular grid and compared against the original high-resolution Telemac solution. On the studied case, the learned surrogate produces 6-hour predictions in about

0.4\,\mathrm{s}

on a single NVIDIA A100 GPU, compared with about

180\,\mathrm{min}

on 56 CPU cores for the reference simulation. These results support graph-based surrogates as practical complements to industrial hydraulic solvers for operational flood mapping.

Abstract

Geometry-Aware Neural Operators

Explore similar work

Toward an Operational GNN-Based Multimesh Surrogate for Fast Flood Forecasting

Physics-Informed CNN-LSTM for Street-Scale Urban Flood Prediction: Reconciling Aggregate Accuracy and Street-Level Plausibility

Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations