School of Civil and Environmental Engineering

Ph.D. Thesis Defense Announcement

Physics-Informed Deep Learning for Groundwater Inverse Modeling of Hydraulic Tomography

By: Quan Guo

Advisor: Dr. Jian Luo (CEE)

Committee Members:  Dr. Jingfeng Wang (CEE), Dr. Haiying Huang (CEE), Dr. Chris Chungkei Lai (CEE), Dr. Guanghui (George) Lan (ISYE)

Date and Time:   Thursday, November 16th, 2023, 3:00 PM - 5:00 PM ET

Location:(Hybrid) Mason 2119 and Zoom: https://gatech.zoom.us/j/5021978057?pwd=UUxaNEhUdXBwUVU1aW50ZjFpUVp6dz09

Zoom Link: https://gatech.zoom.us/j/5021978057?pwd=UUxaNEhUdXBwUVU1aW50ZjFpUVp6dz09
 
Groundwater flow simulation plays a crucial role in understanding subsurface water dynamics. Achieving accurate groundwater flow simulations necessitates solving the groundwater inverse problem, which involves the estimation of spatially varying hydrogeological parameter fields based on indirect observations. Hydraulic tomography (HT), also known as sequential pumping tests, has demonstrated great potential for aquifer characterization with relatively low cost and simple data collection techniques. A common and effective approach to solving HT inverse problems is the gradient-based geostatistical approach (GA). The major challenge faced by GA is its high computational cost when the dimension of the target variable is large for estimating a high-resolution parameter field. In addition, GA is not applicable for non-Gaussian fields featuring factures or channels, notable for their discontinuity. In this thesis, we develop a physics-informed deep learning framework to tackle inverse problems associated with various hydrogeological parameter random fields by utilizing HT observations. 
 
We've developed three models tailored to different scenarios. The first, HT-PINN, focuses on smooth Gaussian Random Fields (GRFs) with Gaussian covariance functions. HT-PINN consists of neural network models for transmissivity and transient or steady-state sequential pumping tests. These models are jointly trained, minimizing a total loss function comprising data fitting errors and PDE constraints, with batch training of collocation points which ensures scalability and robustness. Secondly, for non-smooth GRFs characterized by exponential covariance functions, we've integrated Fourier Neural Operator (FNO) with the Reformulated Geostatistical Approach (RGA). FNO serves as a neural network surrogate forward model, trained to solve groundwater Partial Differential Equations (PDEs) efficiently. RGA harnesses geostatistical information and prior distributions. FNO's auto-differentiation eliminates the need for iterative forward simulations, making the combined FNO-RGA model accurate, efficient, and adaptable for non-smooth GRF inverse modeling. Thirdly, addressing non-Gaussian channel fields, we introduce the HT-INV-NN model. It consists of a Deep Neural Network (DNN) predictor and a Generative Adversarial Network (GAN) decoder. The DNN learns the inverse process, mapping hydraulic head measurements to latent variables of random fields, while the GAN reconstructs high-dimensional non-Gaussian channel fields from these latent variables. Our approach reframes the inverse problem as a predictive one, significantly enhancing efficiency while maintaining satisfactory accuracy.