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[2509.19929] Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later
Summary
The paper presents Geometric Autoencoders for Bayesian Inversion (GABI), a novel framework for uncertainty quantification in engineering, leveraging geometry-aware generative models to enhance inference from limited observations.
Why It Matters
This research addresses the critical challenge of recovering information from noisy observations in engineering systems with complex geometries. By introducing GABI, the authors provide a solution that improves predictive accuracy and uncertainty quantification, which is essential for reliable engineering applications.
Key Takeaways
- GABI framework utilizes geometry-aware generative models for Bayesian inversion.
- The approach allows for effective inference from limited and noisy observations.
- Predictive accuracy is comparable to deterministic supervised learning methods.
- Uncertainty quantification is robust and well-calibrated for complex geometries.
- The method is architecture agnostic and efficient, leveraging modern GPU hardware.
Statistics > Machine Learning arXiv:2509.19929 (stat) [Submitted on 24 Sep 2025 (v1), last revised 26 Feb 2026 (this version, v2)] Title:Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later Authors:Arnaud Vadeboncoeur, Gregory Duthé, Mark Girolami, Eleni Chatzi View a PDF of the paper titled Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later, by Arnaud Vadeboncoeur and 3 other authors View PDF HTML (experimental) Abstract:Uncertainty Quantification (UQ) is paramount for inference in engineering. A common inference task is to recover full-field information of physical systems from a small number of noisy observations, a usually highly ill-posed problem. Sharing information from multiple distinct yet related physical systems can alleviate this ill-possendess. Critically, engineering systems often have complicated variable geometries prohibiting the use of standard multi-system Bayesian UQ. In this work, we introduce Geometric Autoencoders for Bayesian Inversion (GABI), a framework for learning geometry-aware generative models of physical responses that serve as highly informative geometry-conditioned priors for Bayesian inversion. Following a ''learn first, observe later'' paradigm, GABI distills information from large datasets of systems with varying geometries, without requiring knowledge of governing PDEs, boundary conditions, or observation processes, into a rich latent prior. At inference time, this prior is seamless...