Title:
ENHANCING INVERSE MODELING IN HYDROGEOLOGY WITH MODERN MACHINE LEARNING ALGORITHMS

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Liu, Ming
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Luo, Jian
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Abstract
Inverse estimation of spatially distributed parameter fields plays an important role in many scientific disciplines including hydrogeology, geophysics, earth science, environmental engineering, etc. Classic stochastic sampling approaches such as Markov Chain Monte Carlo (MCMC) and optimization approaches such as geostatistical approach (GA) can solve inverse problems with a modest number of unknowns. However, we may face challenges when it comes to large-scale, highly heterogeneous fields or fields with special characteristics, such as connected preferential paths. In this thesis, firstly, we develop a new data augmentation approach, i.e., fast conditional image quilting to synthesize realizations based on limited measurements; and this approach is later used to generate channelized training images to support the inverse modeling research study. Secondly, unlike MCMC and optimization approaches that require many forward model evaluations in each iteration, we develop two neural network inverse models on full dimensions (NNI) and principal components (NNPCI) to directly explore the inverse relationships between indirect measurements such as hydraulic heads and the underlying parameter fields such as hydraulic conductivity. We successfully apply our neural network models to large-scale hydraulic tomography experiments to estimate spatially distributed hydraulic conductivity. In particular, with the help of principal component analysis (PCA), the number of neurons in the last layer of NNPCI is the same as that of retained principal components, thus further accelerating the algorithm and making the system scalable regardless of large-scale unknown field parameters. NNI also demonstrates satisfactory inverse results on full dimensions for both Gaussian and non-Gaussian fields with channelized patterns. The major computational advantage for NNI and NNPCI is that the training data can be generated by independent forward model simulations that can be done efficiently using parallel computing. Finally, to account for errors from different sources, including input errors, model structure errors, model parameters errors, etc., we incorporate Bayesian theorem to the neural network models for uncertainty analysis. The system behaves more stably and consistently on varying spatial and temporal scales. The developed approaches are successfully validated with synthetic and field cases.
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2021-08-02
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