Multiiphysics karst flow and transport modelling: From the classical numerical to the novel machine learning approaches

Karst aquifers provide vulnerable water resources accounting for 25 % of the world groundwater resources. Croatian karst aquifers are also well known as highly karstified aquifers presenting very valuable and sensitive water resources. State of the art of the karst flow and transport modelling indicates that only hybrid distributed models, also known as hydrological integrated flow and transport models, can potentially resolve complex karst Multiphysics, especially interrelation between matrix and conduit exchange flow dynamics. However, there are many limitations of distributed hydrological karst models to successful application in practice, especially at the scale of whole watershed. The main problem is requirement for so many parameters and measurements to completely describe complex karst processes. Despite progress of computational resources, hydraulic and specially geophysics equipment and measurement technologies, lot of information usually remain unresolved. The most missing information are usually matrix heterogeneity distribution (i.e. hydraulic conductivity, sorption, porosity), unsaturated (i.e. Van Genunchten) parameters and conduit network structure (depth, spatial location of conduits and/or its diameters and dimensions). Computationally expensive numerical distributed hydrological karst models could be replaced by surrogate models such as deep learning neural networks (for instance see review of Herrmann and Kollmansberger, 2024). Therefore, we discuss here Multiphysics modelling of flow and transport karst process from the classical analytical and numerical approaches to the novel machine learning approaches such as Physical Informed Neural Network - PINN. Particularly, novel advantages of inverse PINN modelling are discussed, especially due to parameter deduction, uncertainty quantification and modelling efficiency.