Geometry-Aware Neural Operators

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A Geometry-Informed Neural Operator surrogate of LISFLOOD-FP for rapid pluvial-fluvial flood forecasting: the case of Forlì, Italy
Nov 2, 2026Samuele Maria Garofalo, Fabio Limardo, Simonetta Bodojra +2Geometry-Aware Neural Operators Flood Forecasting
Data Reply, Turin, Italy · NVIDIA, Santa Clara, CA, USA · University of Virginia, USA
Architecture-Aware Mixed Precision for Replica-Exchange Training of Geometry-Aware Neural Operators with Uncertainty Quantification
Nov 2, 2026Ujin Jeon, Michael Penwarden, Wenqian Chen +1Mixed-Precision Training Geometry-Aware Neural Operators
Department of Electrical and Computer Engineering, Purdue University, West Lafayette, 47907, IN, USA · Sandia National Laboratories, 1515 Eubank Blvd SE, Albuquerque, 87123, NM, USA · Pacific Northwest National Laboratory, 3335 Innovation Blvd, Richland, 99354, WA, USA +1
Geometry-Aware Operator Families for Structured Representation Learning
Sep 27, 2026Zuyuan Zhang, Fei Xu Yu, Tian LanGeometry-Aware Neural Operators Representation Learning
The George Washington University
PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations
Jul 9, 2026Weiheng Zhong, Jing Bi, Victor Oancea +1PDE Surrogate Modeling PDE Operator Learning
Department of Civil and Environmental Engineering, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US · Dassault Systemes Americas, Johnston, RI, US · Siebel School of Computing and Data Science, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US
High-Fidelity Industrial Crash Dynamics Prediction via Geometry-Aware Operator Learning with Memory-Efficient Low-Rank Attention
May 26, 2026Deepak Akhare, Mohammad Amin Nabian, Corey Adams +2Low-Rank Attention Surrogate Modeling
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN · NVIDIA, San Jose, CA · General Motors, Detroit, MI
CATO: Charted Attention for Neural PDE Operators
May 9, 2026Chun-Wun Cheng, Sifan Wang, Carola-Bibiane Schönlieb +1PDE Operator Learning Attention Mechanisms
DAMTP University of Cambridge · Institute for Foundations of Data Science Yale University · Yau Mathematical Sciences Center Tsinghua University
Geometric Neural Operators via Lie Group-Constrained Latent Dynamics
Feb 18, 2026Jiaquan Zhang, Fachrina Dewi Puspitasari, Songbo Zhang +7Geometry-Aware Neural Operators Neural PDE Solvers
School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China · Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China · Institute of Software Chinese Academy of Sciences, Beijing, China +2
PGOT: A Physics-Geometry Operator Transformer for Complex PDEs
Dec 29, 2025Zhuo Zhang, Xi Yang, Ying Miao +5Neural PDE Solvers PDE Surrogate Modeling
National University of Defense Technology · Peking University · National University of Singapore +2

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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+1

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

Geometry-Aware Neural Operators Flood Forecasting Neural Surrogate Modeling Flood Inundation Mapping Neural Operators

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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.