# GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations

arXiv: https://arxiv.org/abs/2202.08956 · HTML: https://mlsanity.com/paper/2202.08956/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)
- [InSituNet: Deep Image Synthesis for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/1908.00407/) (2019)
- [Modeling Local Geometric Structure of 3D Point Clouds using Geo-CNN](https://mlsanity.com/paper/1811.07782/) (2018)
- [A Generative Model for Volume Rendering](https://mlsanity.com/paper/1710.09545/) (2017)
- [A Survey on ML4VIS: Applying Machine Learning Advances to Data Visualization](https://mlsanity.com/paper/2012.00467/) (2020)
- [DeepSphere: towards an equivariant graph-based spherical CNN](https://mlsanity.com/paper/1904.05146/) (2019)
- [NNVA: Neural Network Assisted Visual Analysis of Yeast Cell Polarization Simulation](https://mlsanity.com/paper/1904.09044/) (2019)

## Built on by (most cited first, 30 of 32)

- [DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization](https://mlsanity.com/paper/2204.06504/) (2022)
- [Generative AI for Visualization: State of the Art and Future Directions](https://mlsanity.com/paper/2404.18144/) (2024)
- [VDL-Surrogate: A View-Dependent Latent-based Model for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/2207.13091/) (2022)
- [Efficient deep data assimilation with sparse observations and time-varying sensors](https://mlsanity.com/paper/2310.16187/) (2023)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [A Hierarchical Spatial Transformer for Massive Point Samples in Continuous Space](https://mlsanity.com/paper/2311.04434/) (2023)
- [Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration](https://mlsanity.com/paper/2504.00904/) (2025)
- [ParamsDrag: Interactive Parameter Space Exploration via Image-Space Dragging](https://mlsanity.com/paper/2407.14100/) (2024)
- [SurroFlow: A Flow-Based Surrogate Model for Parameter Space Exploration and Uncertainty Quantification](https://mlsanity.com/paper/2407.12884/) (2024)
- [Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint](https://mlsanity.com/paper/2409.00458/) (2024)
- [Learning CO2 plume migration in faulted reservoirs with Graph Neural Networks](https://mlsanity.com/paper/2306.09648/) (2023)
- [Uncertainty-Aware Deep Neural Representations for Visual Analysis of Vector Field Data](https://mlsanity.com/paper/2407.16119/) (2024)
- [Uncertainty-Informed Volume Visualization using Implicit Neural Representation](https://mlsanity.com/paper/2408.06018/) (2024)
- [Beyond Grid Data: Exploring Graph Neural Networks for Earth Observation](https://mlsanity.com/paper/2411.03223/) (2024)
- [Deep learning and multi-level featurization of graph representations of microstructural data](https://mlsanity.com/paper/2210.00854/) (2022)
- [HAiVA: Hybrid AI-assisted Visual Analysis Framework to Study the Effects of Cloud Properties on Climate Patterns](https://mlsanity.com/paper/2305.07859/) (2023)
- [Visual Analysis of Prediction Uncertainty in Neural Networks for Deep Image Synthesis](https://mlsanity.com/paper/2406.18545/) (2024)
- [Minority Report: A Graph Network Oracle for In Situ Visualization](https://mlsanity.com/paper/2206.12683/) (2022)
- [Deep Learning for Spatiotemporal Big Data: A Vision on Opportunities and Challenges](https://mlsanity.com/paper/2310.19957/) (2023)
- [ConfEviSurrogate: A Conformalized Evidential Surrogate Model for Uncertainty Quantification](https://mlsanity.com/paper/2504.02919/) (2025)
- [Topology Guidance: Controlling the Outputs of Generative Models via Vector Field Topology](https://mlsanity.com/paper/2505.06804/) (2025)
- [FA-INR: Adaptive Implicit Neural Representations for Interpretable Exploration of Simulation Ensembles](https://mlsanity.com/paper/2506.06858/) (2025)
- [SWR-Viz: AI-assisted Interactive Visual Analytics Framework for Ship Weather Routing](https://mlsanity.com/paper/2511.15182/) (2025)
- [GS-Surrogate: Deformable Gaussian Splatting for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/2604.06358/) (2026)
- [Quantifying the Impact of Lossy Compression on Neural Generative Surrogate Modeling](https://mlsanity.com/paper/2606.15959/) (2026)
- [SOLAR: A Highly Optimized Data Loading Framework for Distributed Training of CNN-based Scientific Surrogates](https://mlsanity.com/paper/2211.00224/) (2022)
- [Neural Stream Functions](https://mlsanity.com/paper/2307.08142/) (2023)
- [Seeing the Many: Exploring Parameter Distributions Conditioned on Features in Surrogates](https://mlsanity.com/paper/2508.13088/) (2025)
- [Compressive Modeling and Visualization of Multivariate Scientific Data using Implicit Neural Representation](https://mlsanity.com/paper/2510.15535/) (2025)
- [Refine Now, Query Fast: A Decoupled Refinement Paradigm for Implicit Neural Fields](https://mlsanity.com/paper/2602.15155/) (2026)

## Abstract (arXiv)

We propose GNN-Surrogate, a graph neural network-based surrogate model to explore the parameter space of ocean climate simulations. Parameter space exploration is important for domain scientists to understand the influence of input parameters (e.g., wind stress) on the simulation output (e.g., temperature). The exploration requires scientists to exhaust the complicated parameter space by running a batch of computationally expensive simulations. Our approach improves the efficiency of parameter space exploration with a surrogate model that predicts the simulation outputs accurately and efficiently. Specifically, GNN-Surrogate predicts the output field with given simulation parameters so scientists can explore the simulation parameter space with visualizations from user-specified visual mappings. Moreover, our graph-based techniques are designed for unstructured meshes, making the exploration of simulation outputs on irregular grids efficient. For efficient training, we generate hierarchical graphs and use adaptive resolutions. We give quantitative and qualitative evaluations on the MPAS-Ocean simulation to demonstrate the effectiveness and efficiency of GNN-Surrogate. Source code is publicly available at https://github.com/trainsn/GNN-Surrogate.