Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification

Abstract

Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based surrogate method is developed for the forward model to allow us to solve efficiently such high-dimensional inverse problems. The surrogate is trained using limited evaluations of the forward model. Since the relationship between the time-varying inputs and outputs of the forward transport model is complex, we propose an autoregressive strategy, which treats the output at the previous time step as input to the network for predicting the output at the current time step. We employ a dense convolutional encoder-decoder network architecture in which the high-dimensional input and output fields of the model are treated as images to leverage the robust capability of convolutional networks in image-like data processing. An iterative local updating ensemble smoother (ILUES) algorithm is used as the inversion framework. The proposed method is evaluated using a synthetic contaminant source identification problem with 686 uncertain input parameters. Results indicate that, with relatively limited training data, the deep autoregressive neural network consisting of 27 convolutional layers is capable of providing an accurate approximation for the high-dimensional model input-output relationship. The autoregressive strategy substantially improves the network's accuracy and computational efficiency. The application of the surrogate-based ILUES in solving the inverse problem shows that it can achieve accurate inversion results and predictive uncertainty estimates.

arXiv comment30 pages, 21 figures, submitted to Water Resources Research

References in corpus (11)

• A trans-disciplinary review of deep learning research for water resources scientists
• Roulette-wheel selection via stochastic acceptance
• Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
• Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification
• Simulation-based optimal Bayesian experimental design for nonlinear systems
• Training-image based geostatistical inversion using a spatial generative adversarial neural network
• Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media
• Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network
• An iterative local updating ensemble smoother for estimation and uncertainty assessment of hydrologic model parameters with multimodal distributions
• Discovering state-parameter mappings in subsurface models using generative adversarial networks
• Comparing seven variants of the Ensemble Kalman Filter: How many synthetic experiments are needed?

Cited by in corpus (24)

• Surrogate Modeling for Fluid Flows Based on Physics-Constrained Deep Learning Without Simulation Data
• A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems
• Deep Learning of Subsurface Flow via Theory-guided Neural Network
• Deep-learning-based surrogate flow modeling and geological parameterization for data assimilation in 3D subsurface flow
• Integration of adversarial autoencoders with residual dense convolutional networks for estimation of non-Gaussian hydraulic conductivities
• Multiphase flow prediction with deep neural networks
• Improving prediction of the terrestrial water storage anomalies during the GRACE and GRACE-FO gap with Bayesian convolutional neural networks
• Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example
• 3D CNN-PCA: A Deep-Learning-Based Parameterization for Complex Geomodels
• Efficient Uncertainty Quantification for Dynamic Subsurface Flow with Surrogate by Theory-guided Neural Network
• Solving inverse problems using conditional invertible neural networks
• Theory-guided Auto-Encoder for Surrogate Construction and Inverse Modeling
• Using Deep Learning to Improve Ensemble Smoother: Applications to Subsurface Characterization
• Use of Multifidelity Training Data and Transfer Learning for Efficient Construction of Subsurface Flow Surrogate Models
• Markov Chain Monte Carlo with Neural Network Surrogates: Application to Contaminant Source Identification
• Surrogate-Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Error
• Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties
• Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems
• Thermal experiments for fractured rock characterization: theoretical analysis and inverse modeling
• Extended Dynamic Mode Decomposition for Inhomogeneous Problems
• Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls
• Identification of Physical Processes and Unknown Parameters of 3D Groundwater Contaminant Problems via Theory-guided U-net
• Efficient approximation of high-dimensional exponentials by tensornetworks
• Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification