[2603.00393] Dual-space posterior sampling for Bayesian inference in constrained inverse problems

Physics > Geophysics arXiv:2603.00393 (physics) [Submitted on 28 Feb 2026] Title:Dual-space posterior sampling for Bayesian inference in constrained inverse problems Authors:Ali Siahkoohi, Kamal Aghazade, Ali Gholami View a PDF of the paper titled Dual-space posterior sampling for Bayesian inference in constrained inverse problems, by Ali Siahkoohi and Kamal Aghazade and Ali Gholami View PDF HTML (experimental) Abstract:Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface properties by fitting seismic measurements subject to the wave equation, where ill-conditioning is inherent to noisy, band-limited, finite-aperture data and shadow zones. Casting the inverse problem into a Bayesian framework allows for a more comprehensive description of its solution, where instead of a single estimate, the posterior distribution characterizes non-uniqueness and can be sampled to quantify uncertainty. However, no clear procedure exists for translating hard physical constraints, such as the wave equation, into prior distributions amenable to existing sampling techniques. To address this, we perform posterior sampling in the dual space using an augmented Lagrangian formulation, which translates hard constraints into penalties amenable to sampling algorithms while ensuring their exact satisfaction. We achieve this ...