Fig. 1.Study Area (a. China b. Liaoning Province c. Hun River basin d. Sampling sites). Fig. 2.Schematic Diagram of the Multi-Pollution Source Dynamic Weight Allocation Mechanism. Fig. 3.Coupled Identification Framework. Fig. 4.Schematic of the simplified Hun River groundwater model (a) and hydraulic conductivity field (b). Fig. 5.Comparative analysis of simulated and actual values from the groundwater model (a. Water levels b. Mn concentrations in wells exceeding standards). Fig. 6.Numerical simulation results of groundwater (The hydraulic head field (a) and the distribution of the contamination plume at time t=[300,600,900,1200,1500,1800,2100] [T] (b-h). Panels (i) depict the probability of the contamination concentration exceeding the Class III standards of the GB14848–2017 over the simulation period.). Fig. 7.The Mn concentration fields at time t=[300,600,900,1200,1500,1800,2100] [T] (a-g) and hydraulic head field (h) in the study area predicted by the forward model (y) and the AR-Net-WL surrogate model with training sample size n=500 (̃y). The difference between the predictions is denoted by (y−̃y). Fig. 8.The Mn concentration fields at time t=[300,600,900,1200,1500,1800,2100] [T] (a-g) and hydraulic head field (h) in the study area predicted by the forward model (y) and the AR-Net-DA surrogate model with training sample size n=500 (̃y). The difference between the predictions is denoted by (y−̃y). Fig. 9.The frequency distribution of the maximum absolute prediction errors (∣emax∣) for the AR-Net-WL and AR-Net-DA networks. Fig. 10.Accuracy comparison of surrogate models based on different training sample numbers. Fig. 11.The Mn concentration fields at time t=[300,600,900,1200,1500,1800,2100] [T] (a-g) and hydraulic head field (h) in the study area predicted by the forward model (y) and the AR-Net-DA surrogate model with training sample size n=3000 (̃y). The difference between the predictions is denoted by (y−̃y). Fig. 12.The estimates of log hydraulic conductivity field obtained through inversion using the ES-MDA algorithm based on both the original and surrogate models (a represents the true hydraulic conductivity field of the study area; b-d and h-j represent the three posterior estimates; e and k show the estimated means; f and l display the estimated variances). Fig. 13.Six source location parameters{SXj,
SY j}and six pollutant release history parameters{Si j}obtained from the joint ES-MDA inversion based on (a) the original model and (b) the surrogate model (stress period i=1,2; source j=1, 2, 3), with the red dashed lines indicating the true values. | 
