# A Deep Generative Model for the Simulation of Discrete Karst Networks

arXiv: https://arxiv.org/abs/2506.09832 · HTML: https://mlsanity.com/paper/2506.09832/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

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

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- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material](https://mlsanity.com/paper/2304.01565/) (2023)

## Abstract (arXiv)

The simulation of discrete karst networks presents a significant challenge due to the complexity of the physicochemical processes occurring within various geological and hydrogeological contexts over extended periods. This complex interplay leads to a wide variety of karst network patterns, each intricately linked to specific hydrogeological conditions. We explore a novel approach that represents karst networks as graphs and applies graph generative models (deep learning techniques) to capture the intricate nature of karst environments. In this representation, nodes retain spatial information and properties, while edges signify connections between nodes. Our generative process consists of two main steps. First, we utilize graph recurrent neural networks (GraphRNN) to learn the topological distribution of karst networks. GraphRNN decomposes the graph simulation into a sequential generation of nodes and edges, informed by previously generated structures. Second, we employ denoising diffusion probabilistic models on graphs (G-DDPM) to learn node features (spatial coordinates and other properties). G-DDPMs enable the generation of nodes features on the graphs produced by the GraphRNN that adhere to the learned statistical properties by sampling from the derived probability distribution, ensuring that the generated graphs are realistic and capture the essential features of the original data. We test our approach using real-world karst networks and compare generated subgraphs with actual subgraphs from the database, by using geometry and topology metrics. Our methodology allows stochastic simulation of discrete karst networks across various types of formations, a useful tool for studying the behavior of physical processes such as flow and transport.