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

arXiv: https://arxiv.org/abs/1812.09444 · HTML: https://mlsanity.com/paper/1812.09444/

## Key facts

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

## Built on by (most cited first, 26 of 26)

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- [Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls](https://mlsanity.com/paper/2310.06319/) (2023)
- [Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties](https://mlsanity.com/paper/2110.12367/) (2021)
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- [Improving prediction of the terrestrial water storage anomalies during the GRACE and GRACE-FO gap with Bayesian convolutional neural networks](https://mlsanity.com/paper/2101.09361/) (2021)
- [Applications of physics-informed scientific machine learning in subsurface science: A survey](https://mlsanity.com/paper/2104.04764/) (2021)
- [Gaussian process regression and conditional Karhunen-Lo'eve models for data assimilation in inverse problems](https://mlsanity.com/paper/2301.11279/) (2023)
- [GeoFUSE: A High-Efficiency Surrogate Model for Seawater Intrusion Prediction and Uncertainty Reduction](https://mlsanity.com/paper/2410.20118/) (2024)
- [Identification of Physical Processes and Unknown Parameters of 3D Groundwater Contaminant Problems via Theory-guided U-net](https://mlsanity.com/paper/2205.00134/) (2022)
- [Ensemble random forest filter: An alternative to the ensemble Kalman filter for inverse modeling](https://mlsanity.com/paper/2207.03909/) (2022)
- [Bayesian deep learning framework for uncertainty quantification in high dimensions](https://mlsanity.com/paper/2210.11737/) (2022)
- [Deep Learning and Inverse Problems](https://mlsanity.com/paper/2309.00802/) (2023)
- [Optimization of geological carbon storage operations with multimodal latent dynamic model and deep reinforcement learning](https://mlsanity.com/paper/2406.04575/) (2024)
- [Learning multi-phase flow and transport in fractured porous media with auto-regressive and recurrent graph neural networks](https://mlsanity.com/paper/2502.17512/) (2025)

## 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.