Tailings dams are formed through long-term accumulation of tailings, featuring complex stratification and non-uniform permeability coefficients. To obtain representative permeability coefficients that reflect their overall permeability characteristics, a novel inversion method was proposed. Optimal Latin Hypercube Sampling (OLHS) was used to obtain uniformly distributed samples of permeability coefficient combinations for tailings dams. These samples were then input into a finite element model for forward analysis to obtain corresponding samples of water heads at monitoring points. The two sets of samples were combined to form a dataset. A nonlinear mapping relationship from the permeability coefficients to the water heads at monitoring points was established using the Kernel Extreme Learning Machine (KELM). The hyperparameters of the KELM were optimized using an Improved Animated Oat Optimization (IAOO) algorithm, which integrated Latin Hypercube Sampling for population initialization, centroid opposition-based learning, and an adaptive optimal-seeking boundary mechanism. An inversion model for the permeability coefficient of tailings dams based on OLHS-IAOO-KELM was thus established and subsequently applied to a practical engineering case. The permeability coefficient values obtained through the inversion model were reasonable. The relative errors between the calculated water heads from forward seepage analysis and the measured water heads at the seven monitoring points did not exceed 2.08%, meeting the engineering accuracy requirements. Furthermore, the potential distribution of the seepage field in a typical cross-section of the tailings dam conformed to general patterns. Compared with other models, the inversion result of the proposed model exhibited the smallest errors. The proposed model demonstrates high accuracy and robustness, and possesses practical value for the inversion of permeability coefficients in tailings dams.