Towards Efficient High-Dimensional Uncertainty Quantification And Inverse Analysis In Groundwater Modeling Using Deep Learning

Groundwater models are now used widely to predict the effects of future anthropogenic and/or natural occurrences in the subsurface environment.Building an accurate numerical model requires the specification of model parameters.However,direct measurement of the input parameters,such as the heterogeneous permeability field,is usually infeasible.There-fore,they are commonly estimated via inverse modeling based on easily accessible mea-surements of state variables(e.g.,hydraulic heads and solute concentrations).In addition,model predictions are inherently uncertain due to the uncertainties associated with model parameters,initial/boundary conditions,driving forces,etc.It is thus necessary to quan-tify the predictive uncertainty to facilitate science-informed decision making.Uncertainty quantification(UQ)and inverse modeling,however,can be computationally very intensive as many repeated forward model runs are often required.This is especially the case for problems with high-dimensional input parameters and/or for time-consuming models.For such cases it would be very beneficial to use an accurate but much faster-to-run surrogate model to substitute the forward model for the majority of the required model executions.In this study,we propose to incorporate the computationally efficient surrogate meth-ods into traditional UQ and inverse modeling methods,so as to substantially alleviate the computational burden.In particular,we propose a deep learning-based surrogate method to tackle the "curse of dimensionality" for traditional surrogate methods.As a result,the sur-rogate methods can be employed to efficiently perform high-dimensional UQ and inverse modeling in groundwater modeling.The main conclusions are summarized as follows:1.An adaptive surrogate method,in which the informative training samples are adaptively selected,is proposed to efficiently solve the UQ tasks of groundwater models with low-dimensional uncertain parameters.The results of applications in two case studies in-dicate that the adaptive surrogate-based method greatly improves the computational efficiency of UQ.However,applications of the proposed method are limited to low-dimensional problems due to the "curse of dimensionality" for the surrogate method used.2.A deep convolutional encoder-decoder network surrogate method is proposed for map-pings with high-dimensional inputs and outputs.This method successfully tackles the curse of dimensionality by treating the high-dimensional input and output fields as im-ages to leverage the robust capability of convolutional neural networks in image pro-cessing.The proposed method is evaluated using a multiphase flow model with a 2,500-dimensional uncertain permeability field.Results indicate that,with limited training data,the surrogate model is capable of accurately approximating the output pressure and saturation fields and can be efficiently used to compute the statistics of the system responses.3.The proposed deep neural network surrogate method is further applied to a groundwater contaminant source identification problem,which also involves the estimation of hetero-geneous conductivity field.Considering the complex relationship between the output concentration fields and the time-varying source strength,we propose to represent this time-varying process using an autoregressive model.That is,the concentration field at the previous time step is treated as input to predict the current concentration field.This enables the network to better capture the complex input-output relationship.The pro-posed surrogate method is combined with an inverse method.The application results in a source identification problem with 686 uncertain input parameters indicate that the proposed method is able to efficiently obtain accurate inversion results.4.In the last case study,in solute transport models,we are concerned with estimating non-Gaussian conductivity fields.For this kind of problems with highly complex input-output mappings,we adopt in the network a multilevel residual learning structure.This enables us to build deeper networks to obtain improved accuracy.In addition,a convolu-tional adversarial autoencoder(CAAE)is propose for parameterization of non-Gaussian conductivity fields.The surrogate method and the parameterization method are com-bined with an inverse method to formulate an efficient inversion framework.The in-tegrated method is demonstrated using 2-D and 3-D solute transport models with non-Gaussian conductivity fields.The results suggest that this framework can efficiently pro-vide accurate inversion results in problems with high-dimensional(3,200 and 12,288)non-Gaussian conductivity fields.The increased computational efficiency in solving high-dimensional uncertainty quan-tification and inverse modeling enables us to use more accurate but computationally more expensive forward models in practical applications of groundwater management.