为了解决地下水模型反演的高耗时问题,提出了一种可快速识别非稳态渗透系数的耦合反演算法。该算法将参数反演过程与降阶模型训练相耦合,用降阶模型替代原始模型从而减少总反演耗时。为了使降阶模型能准确捕捉原始模型在时域上的响应特征,采用均匀策略法对时间步快照进行采集。基于耦合反演算法的特点,通过计算最优参数对应的降阶解在时域内各节点的相对误差,以最大误差值小于预设阈值为迭代终止条件。以一个二维抽水井模型为例,将该方法与基于原始模型的反演方法进行了对比。结果表明: 在取得相当的反演精度的前提下,该方法可节省约95.38%的计算耗时。此外,在不同观测误差、网格密度及反演维数条件下,该方法的反演结果与原始模型一致,而计算耗时均小于原始模型的5%,且对“维数诅咒”问题具有更强的鲁棒性。因此,该方法显著提升了参数反演的计算效率,具有良好的工程应用前景。

[Objective] During the parameter inversion process of groundwater models, frequent calls to the forward model result in excessive computational demand and prolonged processing time, which severely limits their practical applicability. To address the high time consumption in groundwater model inversion, this study proposes a coupled inversion algorithm capable of rapidly identifying unsteady permeability coefficients. [Methods] The proposed algorithm coupled the parameter inversion process with reduced-order model training, where the reduced-order model was employed instead of the original model for parameter inversion calculation, thereby reducing total inversion time. During the iteration process, the sum of squared errors between the reduced-order model calculation values and observations was used as the objective function, and an improved differential evolution algorithm with strong global search capability was employed as the optimization method for parameter inversion. In each iteration, the parameters that best matched the observations were identified as optimal, and snapshots of these optimal parameters were calculated to train the reduced-order model, thereby enhancing the inversion accuracy in the next generation. To enable the reduced-order model to accurately capture the time-domain response characteristics of the original model, a uniform snapshot strategy was employed to collect time-step snapshots. Based on the characteristics of the coupled inversion algorithm, the relative error of the reduced-order solution corresponding to the optimal parameters was calculated at all nodes within the time domain, and iteration was terminated when the maximum error fell below a preset threshold. [Results] Taking a two-dimensional pumping well model as an example, the proposed method was compared with an inversion approach based on the original model. The results indicated that: (1) For unsteady seepage parameter inversion, compared with the optimal time snapshot strategy, using a uniform snapshot collection strategy to construct the reduced-order model could achieve higher computational accuracy, while the reduced-order model had a lower average order. (2) While maintaining inversion accuracy comparable to that of the original model, the proposed algorithm could reduce computational time by approximately 95.37%. (3) Near the optimal parameters, the reduced-order model obtained by the proposed method showed almost identical responses to the original model. However, the error increased significantly when moving away from the optimal solution. (4) The effects of observation error, mesh density, and inversion dimensionality on the inversion accuracy of the proposed algorithm were consistent with those of the original model, but the computational time of the proposed algorithm was less than 5% of that of the original model. (5) The proposed algorithm was less affected by the order of the original model, and the increase in the computational time was proportionally smaller than the increase in model order, indicating higher computational efficiency for high-order models than for low-order ones. (6) Compared with low-dimensional inversion problems, the proposed algorithm exhibited greater time-saving efficiency in handling high-dimensional cases, suggesting stronger robustness against the curse of dimensionality. (7) Under different convergence accuracies, the proposed algorithm could consistently reproduce the results of the original model without a significant increase in computational time even as accuracy improved. [Conclusion] The proposed coupled inversion algorithm in this study, as a deterministic finite element-based inversion framework, innovatively couples the training process of the reduced-order model with the parameter inversion process and significantly improves the computational efficiency of parameter inversion.Characterized by a simple structure,ease of implementation, and no need for posterior error calculation,the algorithm has significant engineering application value and promising prospects for broad application.