Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification (1812.09444v1)

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.

• The paper presents a framework leveraging deep autoregressive neural networks integrated with an iterative local updating ensemble smoother (ILUES) algorithm to solve high-dimensional inverse problems for identifying groundwater contaminant sources and hydraulic conductivity efficiently.
• The results demonstrate high approximation accuracy on a 686-dimensional problem with limited training data, enabling accurate inversion and credible uncertainty estimates with reduced computational cost.
• The findings advance practical applications of deep learning in environmental and geoscientific modeling, enabling more efficient and accurate solutions for complex subsurface systems and potential real-time decision-making.

Deep Autoregressive Neural Networks for High-Dimensional Inverse Problems in Groundwater Contaminant Source Identification

The paper presents an advanced methodological framework leveraging deep autoregressive neural networks for solving high-dimensional inverse problems related to groundwater contaminant source identification. The research addresses the challenge of identifying both the contaminant source and the hydraulic conductivity in highly heterogeneous media, which is inherently a high-dimensional problem due to the complex interdependencies and variabilities in subsurface parameters.

Methodological Innovation

The authors propose a novel surrogate modeling approach employing deep autoregressive neural networks integrated with an iterative local updating ensemble smoother (ILUES) algorithm. The surrogate model is crafted to replace the traditional forward model, significantly enhancing computational efficiency while maintaining a high level of accuracy. By framing the surrogate modeling as an image-to-image regression task, the authors exploit the power of dense convolutional encoder-decoder networks to handle the high dimensionality of the input and output spaces. This approach inherently tackles the curse of dimensionality, a common bottleneck in traditional surrogate modeling methods.

A pivotal aspect of the methodology is the autoregressive strategy utilized to capture the temporal evolution of contaminant transport. The autoregressive model considers the output at the previous time step as an input for the current prediction, effectively capturing the dynamic relationship in the data sequence. The network architecture, consisting of 27 convolutional layers, is structured to enhance feature representation, particularly in handling the spatial complexity of the hydraulic conductivity field and contaminant concentrations.

Numerical Results and Implications

The method is assessed through a synthetic problem setup involving a 686-dimensional inverse problem. The results demonstrate that the proposed deep autoregressive neural network can achieve high approximation accuracy with relatively limited training data. Particularly noteworthy is the model's performance, even in regions of high nonlinearity near the contaminant source. The precision and reliability of the surrogate model facilitate accurate inversion results and credible predictive uncertainty estimates with a significant reduction in computational cost.

The paper's findings have profound implications for advancing the practical applications of deep learning in environmental and geoscientific modeling. The methodological innovation not only enhances computational efficiency but also sets a foundation for future explorations into more complex, high-dimensional subsurface systems. By integrating deep learning with probabilistic frameworks, there is potential for improved real-time decision-making in environmental monitoring and management.

Future Directions

This research paves the way for further advancements and applications in engineering and environmental sciences. The integration of adaptive and transfer learning techniques could further improve the network's efficiency and applicability across various domains and datasets. In addition, coupling this approach with observational data assimilation could offer robust solutions to other nonlinear dynamical systems in hydrology and beyond, where traditional methods fall short due to computational constraints.

In conclusion, the paper presents a sophisticated and practical solution to high-dimensional inverse problems in subsurface hydrology, promising new trajectories in artificial intelligence-driven geosciences.