Committee Members Information

• Ph.D. Advisor: Tariq Ali Alkhalifa
• External Examiner: Herve Chauris
• Committee Chair: David Keyes
• 4th Committee Member: Bicheng Yan
• 5th Committee Member: George Turkiyyah

Abstract

Seismic imaging and inversion remain fundamentally ill-posed due to band‐limited data, heterogeneous illumination, and strong nonlinearity between the parameters under investigation and the observed data. This dissertation advances a unified path toward stable, generalizable, and uncertainty‐aware solutions by combining physics‐informed neural networks (PINNs), learned generative priors, and scalable Bayesian inference. I pursue four objectives: (i) stable and efficient neural PDE solvers; (ii) generalization across parameter distributions without retraining; (iii) adaptive, geologically plausible regularization for multi‐parameter inversion; and (iv) data‐fidelity–guided posterior sampling that is computationally tractable for large-scale seismic applications.

First, I stabilize PINN traveltime tomography by enforcing boundary data and measurements as hard constraints. Using the theory of functional connections and an additive traveltime factorization, I reduce the usual multi‐term PINN loss into a single physically coherent objective. The resulting solver converges more stably than its soft constraint counterpart in 2D and 3D, handles sparse/irregular picks and topography, and provides a mesh‐independent forward operator suitable for downstream inversion.

Second, I develop LatentPINNs to amortize solutions over families of models. I learn compact latent codes for PDE parameters and condition a single physics‐informed surrogate on these codes, so solutions become functions of both coordinates and parameter latents. I extend this idea to produce multiple wavefield solutions from a single training and bring the idea inside full‐waveform inversion (FWI) by updating only the latent variables while keeping the encoder/decoder and solver fixed. Across representative tests (eikonal, scattered Helmholtz, and FWI), these strategies retain physical fidelity, reduce search dimension, and deliver substantial speedups and lower misfit relative to per‐instance training and conventional FWI.

Third, I replace conventional hand‐crafted regularization in elastic FWI with learned diffusion model priors. An unsupervised diffusion model over elastic moduli captures both marginal structure and realistic cross‐parameter coupling, acting as a plug‐and‐play regularizer during inversion. I further make sampling wavenumber‐aware: low‐wavenumber structure is injected early, high‐wavenumber detail later, mirroring FWI’s spectral progression. On synthetic and land field data, this improves elastic‐ratio stability, reduces cross‐talk, enhances data fit, and mitigates acquisition footprint effects—even with single‐component recordings.

Finally, I address calibrated uncertainty with the aim of practicality. I initialize Stein variational gradient descent (SVGD) with reconstruction‐guided diffusion samples conditioned on seismic migration images, which concentrates particles near posterior support and reduces forward/adjoint solves. I also develop a diffusion‐based posterior sampler tailored to field‐scale FWI with simultaneous‐source (encoded‐shot) likelihood guidance, annealed level transitions, and light Langevin refinements in model space. The resulting posteriors yield interpretable means and variances that reflect data illumination, pass standard posterior predictive checks, and outperform strong variational baselines in accuracy–cost trade‐off.

Taken together, these contributions show that physics‐informed surrogates, latent representation learning, and diffusion‐driven inference can be composed into a coherent workflow for large‐scale seismic inversion: forward models become stable and reusable; priors become adaptive and geological; and uncertainty quantification becomes doable—without abandoning data fidelity or computational feasibility.