Deep generative models for solving geophysical inverse problems

My thesis presents several novel methods to facilitate solving large-scale inverse problems by utilizing recent advances in machine learning, and particularly deep generative modeling. Inverse problems involve reliably estimating unknown parameters of a physical model from indirect observed data that are noisy. Solving inverse problems presents primarily two challenges. The first challenge is to capture and incorporate prior knowledge into ill-posed inverse problems whose solutions cannot be uniquely identified. The second challenge is the computational complexity of solving inverse problems, particularly the cost of quantifying uncertainty. The main goal of this thesis is to address these issues by developing practical data-driven methods that are scalable to geophysical applications in which access to high-quality training data is often limited. There are six papers included in this thesis. A majority of these papers focus on addressing computational challenges associated with Bayesian inference and uncertainty quantification, while others focus on developing regularization techniques to improve inverse problem solution quality and accelerate the solution process. These papers demonstrate the applicability of the proposed methods to seismic imaging, a large-scale geophysical inverse problem with a computationally expensive forward operator for which sufficiently capturing the variability in the Earth's heterogeneous subsurface through a training dataset is challenging. The first two papers present computationally feasible methods of applying a class of methods commonly referred to as deep priors to seismic imaging and uncertainty quantification. I also present a systematic Bayesian approach to translate uncertainty in seismic imaging to uncertainty in downstream tasks performed on the image. The next two papers aim to address the reliability concerns surrounding data-driven methods for solving Bayesian inverse problems by leveraging variational inference formulations that offer the benefits of fully-learned posteriors while being directly informed by physics and data. The last two papers are concerned with correcting forward modeling errors where the first proposes an adversarially learned postprocessing step to attenuate numerical dispersion artifacts in wave-equation simulations due to coarse finite-difference discretizations, while the second trains a Fourier neural operator surrogate forward model in order to accelerate the qualification of uncertainty due to errors in the forward model parameterization.