Karst network simulation with statistical learning

A key factor controling flow and solute transport in karstic aquifers is the connectivity of karst networks over long distances. However, in many situations the geometry and position of the karst network is unknown and hard to detect with indirect methods such as geophysics. This is the reason why several Discrete Karst Network (DKN) simulation techniques have been developped in the last decade. Some methods are based on statistical principles (subnetworks of percolation clusters for example). Other methods are based on pseudo-genetic principles.

In this presentation, we explore the possibility to learn the structure of karst networks from a large data set of geometries acquired by cavers and simulate new networks using generative statistical learning techniques. So far, the best results are obtained by combining a recurrent neural network that is capable of simulating the topology of the network (adjencency matrix), and a denoising diffusion probability model on graph to generate the spatial position of the nodes. This technique is capable to produce networks having similar patterns and geometry as the ones used in the training phase. The resulting networks can be used as input for the simulation of flow and transport.