A Deep Generative Model for the Simulation of Discrete Karst Networks

TL;DR

This paper introduces a novel deep learning framework combining graph recurrent neural networks and diffusion models to simulate realistic discrete karst networks, capturing their complex topology and spatial features for physical process analysis.

Contribution

It presents a new graph-based generative approach for simulating discrete karst networks, integrating topological and spatial feature learning with realistic graph generation.

Findings

Generated networks match real-world data in geometry and topology.

The model effectively captures diverse karst network patterns.

Stochastic simulations aid in studying flow and transport processes.

Abstract

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.