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• A novel framework IGSM for heterogeneous steady-state parameter inversion problems. • Coupling of group evolutionary algorithm and reduced-order model. • IGSM is fast, simple, reliable and requires no posterior error estimation. • Results of IGSM are less affected by the density and parameter variation range. • IGSM can quickly solve the parameter inversion of large-scale steady state problems. To solve the time-consuming parameter inversion problem based on swarm evolution algorithm, this study proposes an improved greedy sampling method (GSM) (IGSM) based on model reduction technology to rapidly estimate the hydraulic conductivity of steady-state seepage problem. Different from the traditional GSM, IGSM neither needs to estimate the posterior error bound of the reduced-order model (ROM) nor does it require a training sample set to train the ROM. Instead, the observation data are directly applied to the training process of ROM. Each iterative process of IGSM includes a parameter inversion process to obtain the parameters that best match the observation information and use it to update the current ROM. The improved differential evolution algorithm (e.g., MMRDE) is used as the search algorithm, and the resulting algorithm is denoted as IGSM-MMRDE. After comparative testing, IGSM-MMRDE was found to have higher accuracy and lower calculation cost than GSM-MMRDE. In addition, IGSM-MMRDE is also capable of high-dimensional parameter inversion problems and parameter inversion with a wider search range. After applying IGSM-MMRDE to the inversion of the rock mass hydraulic conductivity of the natural seepage field in the dam site area of a hydropower station, IGSM-MMRDE converges quickly and takes much less time than ADINA-MMRDE based on the full-order model (approximately 0.31% of ADINA-MMRDE). The performance results are even better than the ADINA-MMRDE using the fixed evolutionary generation. Therefore, the advantages of using IGSM in the rapid inversion of the initial seepage field of large-scale projects are extremely evident. [ABSTRACT FROM AUTHOR]