Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces
arXiv:2603.14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime. Based on one-step generative transport, the method learns an amortized neural operator whose pushforward of a Gaussian source approximates the posterior distribution conditioned on each new observation. We show that white-noise sources are incompatible with the function-space limit, and therefore adopt a prior-aligned GRF as the source. We justify this choice through the Lipschitz regularity of the resulting one-step conditional posterior
The continuous advancements in generative modeling and neural operators are enabling new approaches to complex statistical problems in AI.
This development improves the efficiency and accuracy of solving Bayesian inverse problems, which are critical for various scientific and engineering applications, by directly addressing the function-space regime.
The ability to accurately model posterior distributions in function spaces with a more compatible source model will enhance the reliability and applicability of AI in scientific discovery and data assimilation.
- · AI researchers (Machine Learning)
- · Engineers (Inverse Problems)
- · Scientific Computing community
- · Traditional probabilistic programming methods
- · Less efficient inverse problem solvers
Improved performance and broader application of generative models in complex scientific data analysis.
Accelerated progress in fields requiring robust inverse problem solutions, such as medical imaging, geophysics, and material science.
Potentially enables new forms of autonomous scientific research and discovery through more accurate and efficient AI-driven inference.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG