mlsanityData to 14 Oct 2026

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

arXiv 1812.09444 ↗First posted 22 Dec 2018stat.ML cs.LGcited by 26

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Abstract (arXiv)

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.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). First posted on arXiv 22 Dec 2018.

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Citing papers per year: 2021: 8; 2022: 6; 2023: 5; 2024: 5; 2025: 2.

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  1. 2022Semi-supervised Invertible Neural Operators for Bayesian Inverse Problemscited by 25
  2. 2021Transfer Learning on Multi-Fidelity Datacited by 18
  3. 2021Manifold learning-based polynomial chaos expansions for high-dimensional surrogate modelscited by 16
  4. 2021Bayesian multiscale deep generative model for the solution of high-dimensional inverse problemscited by 12
  5. 2022Use of Multifidelity Training Data and Transfer Learning for Efficient Construction of Subsurface Flow Surrogate Modelscited by 11
  6. 2023Learning a model is paramount for sample efficiency in reinforcement learning control of PDEscited by 6
  7. 2024Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantificationcited by 6
  8. 2021Uncertainty quantification for ptychography using normalizing flowscited by 4
  9. 2022Convolutional-Recurrent Neural Network Proxy for Robust Optimization and Closed-Loop Reservoir Managementcited by 4
  10. 2023VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problemscited by 4
  11. 2023Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controlscited by 4
  12. 2021Deep Learning for Simultaneous Inference of Hydraulic and Transport Propertiescited by 3
14 more
  1. 2021Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder networkcited by 3
  2. 2024Deep Learning Framework for History Matching CO2 Storage with 4D Seismic and Monitoring Well Datacited by 3
  3. 2024Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modelingcited by 3
  4. 2025A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutionscited by 3
  5. 2021Improving prediction of the terrestrial water storage anomalies during the GRACE and GRACE-FO gap with Bayesian convolutional neural networkscited by 2
  6. 2021Applications of physics-informed scientific machine learning in subsurface science: A surveycited by 2
  7. 2023Gaussian process regression and conditional Karhunen-Lo'eve models for data assimilation in inverse problemscited by 2
  8. 2024GeoFUSE: A High-Efficiency Surrogate Model for Seawater Intrusion Prediction and Uncertainty Reductioncited by 1
  9. 2022Identification of Physical Processes and Unknown Parameters of 3D Groundwater Contaminant Problems via Theory-guided U-netcited by 0
  10. 2022Ensemble random forest filter: An alternative to the ensemble Kalman filter for inverse modelingcited by 0
  11. 2022Bayesian deep learning framework for uncertainty quantification in high dimensionscited by 0
  12. 2023Deep Learning and Inverse Problemscited by 0
  13. 2024Optimization of geological carbon storage operations with multimodal latent dynamic model and deep reinforcement learningcited by 0
  14. 2025Learning multi-phase flow and transport in fractured porous media with auto-regressive and recurrent graph neural networkscited by 0