Developing an inverse mapping model for groundwater contamination source identification based on Kolmogorov-Arnold networks.

Groundwater contamination source identification (GCSI) aims to use inverse methods to identify essential information such as the location of contamination sources and their release history, which is of significant practical importance for the prevention and remediation of groundwater contamination. Existing studies typically rely on forward modeling frameworks (mapping from contamination source to concentration monitoring data) with iterative optimization for inversion calculations, which suffers from computational inefficiency and solution non-uniqueness. This study proposes a novel and efficient inverse mapping methodology that enables direct inversion for GCSI problems. Specifically, a Kolmogorov-Arnold Networks (KAN) method is combined with a bidirectional mapping strategy and a positive feedback strategy for training samples. This model provides a solution to the GCSI problem by directly linking contamination concentration monitoring values to contamination source characteristics and simulation model parameters. Furthermore, the feasibility of this proposed method is demonstrated through two hypothetical case studies. Two significant advantages of the KAN inverse mapping model are highlighted based on the experimental results. First, the inversion process demonstrates both speed and accuracy. The contamination source characteristics are identified within seconds with a maximum error of 2% for 12 variables in case 1. Besides, the heterogeneous permeability field inversion achieves a spatial correlation coefficient (SCC) of 0.85 in case 2. Second, the KAN inverse mapping model exhibits robustness and the model still remains stable and accurate even with noisy data. In conclusion, the proposed KAN inverse mapping model combined with the described strategies demonstrates sufficient accuracy and efficiency to address the GCSI problem.