Deep Learning Based Inverse Modeling Of Groundwater Reactive Transport Models

The groundwater reactive transport model is a numerical simulation technique that integrates various physical and chemical processes to quantitatively analyze the solute transport and geochemical reaction processes in subsurface systems.It has been widely used in various earth science and environmental science fields.Nevertheless,obtaining the critical parameters for reactive transport models can be challenging,and therefore,inversion simulation using on-site observation data such as hydraulic heads and solute concentrations is necessary.Reactive transport inverse modeling is crucial for reducing parameter uncertainties and accurately characterizing subsurface dynamic processes.It is also significant for conducting numerical simulations at high levels.Data assimilation has become crucial for solving parameter inverse problems in various disciplines.However,reactive transport models are typically strongly nonlinear,and accurately characterizing solute plume diffusion patterns requires full consideration of the heterogeneity of aquifer parameters.As a result,when using traditional data assimilation methods to conduct groundwater reactive transport inversion researches,three main challenges arise: multi-source heterogeneous data assimilation,optimizing the distribution structure of training sample data for surrogate models,and parameter inversion for high-dimensional heterogeneous models.This study addresses the three challenges mentioned above by leveraging the strengths of deep learning methods,particularly in solving strong nonlinear mappings and high-dimensional feature extraction.To this end,we conducted theoretical research in four areas:(1)construction methods for reactive transport surrogate models,(2)establishment and solution methods for inversion optimization models,(3)an adaptive updating strategy(AUS)for parameter inversion results,and(4)high-dimensional heterogeneous parameter inversion algorithms.Subsequently,we applied these theoretical insights to a contaminated site case study.Our findings and insights from this research are presented below.(1)A scheme for constructing reactive transport surrogate models was established based on a two-dimensional convolutional neural network(2D-CNN),aiming to improve the computational efficiency of forward modeling during data assimilation.Our numerical comparisons demonstrate that this surrogate model can achieve synchronous and high-precision prediction of multiple simulated components while also providing greater accuracy in predicting extreme boundary values compared to other surrogate model structures considered in this study.Furthermore,leveraging the advantages of parallel computing under the deep learning framework,the computational efficiency of the surrogate model has been significantly enhanced compared to the original numerical model.(2)This study proposes a scheme for constructing an inversion optimization model using nonlinear programming optimization theory and Bayesian theorem after obtaining the reactive transport surrogate model.To address the challenges of multi-source heterogeneous data assimilation,the tandem neural network architecture(TNNA)algorithm was proposed to solve the inversion optimization model.A comparison between the TNNA algorithm and the traditional standard genetic algorithm is conducted using the Monte Carlo method.The results indicate that the TNNA inversion algorithm achieves significantly higher convergence accuracy than the genetic algorithm with about one order of magnitude.Additionally,the TNNA algorithm shows better fitting performance for each simulated component and higher accuracy in parameter inversion compared to the genetic algorithm.Furthermore,the computational burden required for TNNA to obtain higher convergence accuracy in the inversion results is reduced by a factor of 50 compared to the genetic algorithm.(3)The TNNA-AUS inversion algorithm is proposed by introducing an adaptive updating strategy(AUS)based on the TNNA algorithm to enhance the accuracy of model parameter inversion results and reduce the bias caused by a limited distribution of training samples for the surrogate model during the inversion processes.The theoretical model case study demonstrates that the TNNA-AUS algorithm outperforms the TNNA algorithm in terms of higher accuracy and computational efficiency,with a reduction of2/3 in the number of forward model calls.Furthermore,the parameter inversion results of the Aquia aquifer model show that the TNNA-AUS algorithm has significant advantages over the TNNA algorithm in achieving multi-source heterogeneous data assimilation for multiple simulated components.(4)An integrated inversion algorithm(KLE-CNN-ILUES)is proposed for the highdimensional heterogeneous permeability parameter inversion problems.This algorithm combines Karhunen-Loève expansion(KLE)for parameter dimensionality reduction,CNN based high-dimensional surrogate models,and the iterative local updating ensemble smoother(ILUES)for stochastic inversion.The KLE-CNN-ILUES algorithm contributes to accurately characterizing the distribution of flow fields and improving the prediction accuracy of multi-component solute plume simulations.Applying this algorithm to actual contaminated sites involves constructing a high-dimensional parameter surrogate model by introducing a residual module into CNN,which improves the prediction accuracy by more than twice that of conventional CNN.The KLE-CNN-ILUES method obtained reliable inversion results for heterogeneous permeability parameters.After model calibration,the hydraulic head prediction closely matched their ovservation values.The inversion results reveal the spatial distribution of high and low permeability zones in the study area.(5)A reactive transport model for five contaminate components was developed based on the inversion result of the heterogeneous permeability field.Seventeen model parameters were identified using the proposed TNNA-AUS algorithm.According to the fitting results of concentration data for each component during the calibration and validation periods,the numerical model after inversion correction is robust and capable of providing reliable simulation and prediction results.In summary,this study enriches and expands the theoretical foundation and technical scope of groundwater inverse modeling.The achievement of this study can provide a scientific basis for research on topics such as carbon dioxide geological storage,geological historical evolution processes,safety assessments for nuclear waste disposal,and early warning of groundwater pollutants.