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Abstract Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances in machine learning and variational inference (VI) have lowered this computational barrier by leveraging data-driven learning. Two VI paradigms have emerged that represent different tradeoffs: amortized and non-amortized. Amortized VI can produce fast results but due to generalizing to many observed datasets it produces suboptimal inference results. Non-amortized VI is slower at inference but finds better posterior approximations since it is specialized towards a single observed dataset. Current amortized VI techniques run into a sub-optimality wall that cannot be improved without more expressive neural networks or extra training data. We present a solution that enables iterative improvement of amortized posteriors that uses the same networks architectures and training data. The benefits of our method requires extra computations but these remain frugal since they are based on physics-hybrid methods and summary statistics. Importantly, these computations remain mostly offline thus our method maintains cheap and reusable online evaluation while bridging the optimality gap between these two paradigms. We denote our proposed methodASPIRE-Amortized posteriors withSummaries that arePhysics-based andIterativelyREfined. We first validate our method on a stylized problem with a known posterior then demonstrate its practical use on a high-dimensional and nonlinear transcranial medical imaging problem with ultrasound. Compared with the baseline and previous methods in the literature, ASPIRE stands out as an computationally efficient and high-fidelity method for posterior inference.
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WISER: Multimodal variational inference for full-waveform inversion without dimensionality reduction
We develop a semiamortized variational inference (VI) framework designed for computationally feasible uncertainty quantification in full-waveform inversion to explore the multimodal posterior distribution without dimensionality reduction. The framework is called full-waveform VI via subsurface extensions with refinements (WISER). WISER builds on top of a supervised generative artificial intelligence method that performs approximate amortized inference that is low-cost albeit showing an amortization gap. This gap is closed through nonamortized refinements that make frugal use of wave physics. Case studies illustrate that WISER is capable of full-resolution, computationally feasible, and reliable uncertainty estimates of velocity models and imaged reflectivities.
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- Award ID(s):
- 2203821
- PAR ID:
- 10650138
- Publisher / Repository:
- Society of Exploration Geophysicists https://pubs.geoscienceworld.org/seg/geophysics/article/90/2/A1/651849/WISER-Multimodal-variational-inference-for-full
- Date Published:
- Journal Name:
- GEOPHYSICS
- Volume:
- 90
- Issue:
- 2
- ISSN:
- 0016-8033
- Page Range / eLocation ID:
- A1 to A7
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1190/geo2024-0483.1
