NestyNet. II. Coherent Function-Space Posteriors from Scientific Neural Surrogates (or How to Avoid Expensive MCMC)

[2608.06274] NestyNet. II. Coherent Function-Space Posteriors from Scientific Neural Surrogates (or How to Avoid Expensive MCMC) Skip to main content Search Submit Donate Log in Astrophysics > Instrumentation and Methods for Astrophysics arXiv:2608.06274 (astro-ph) [Submitted on 6 Aug 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: NestyNet. II. Coherent Function-Space Posteriors from Scientific Neural Surrogates (or How to Avoid Expensive MCMC) Authors: Rodrigo Ibata , Wassim Tenachi , Foivos Diakogiannis , Neil Ibata , Anirudh Shankar View PDF HTML (experimental) Abstract: Scientific analyses increasingly use flexible neural networks, but their thousands of correlated parameters make it challenging to interpret the associated uncertainties. Here we develop a low-dimensional posterior for the fitted function itself, for scientific neural surrogates trained with second-order optimization. Linearizing the fitting procedure with respect to the randomized residual rows gives a measurement-to-function transport, the linear map, assembled from the converged Jacobians and Gauss--Newton curvature, that carries measurement perturbations into the function perturbations that refitting would produce. Its leading singular functions define coherent deformation modes. Independent Gaussian coefficients then generate smooth function draws, so that any derived quantity, including those requiring derivatives or integrals of the draw, inherits the posterior. The construction distinguishes repeated-experiment covariance from the local Gauss--Newton/Laplace posterior and propagates both to correlated quantities of scientific interest. The result is conditional on the fit's declared choices (architecture, hyperparameters, active set, and optimization branch), and every fit is certified as converged by checking that a further optimization step would change the fitted predictions by less than a chosen small fraction of the measurement errors. Our primary example is an 800-parameter phase-space distribution function fit for a mock stellar disk. Four uncertainty coordinates, two orders of magnitude fewer than the fitted parameters and stable under refinement of the force basis, capture 99\% of the vertical-force posterior variance, and 4000 coherent draws propagate through the force, total-density, surface-density, and frequency calculations in 0.8s. The method provides a highly efficient route to uncertainty propagation for derivative-dependent scientific inference. Comments: 16 pages 4 figures Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM) ; Computational Physics (physics.comp-ph) Cite as: arXiv:2608.06274 [astro-ph.IM] (or arXiv:2608.06274v2 [astro-ph.IM] for this version) https://doi.org/10.48550/arXiv.2608.06274 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Rodrigo A. Ibata [ view email ] [v1] Thu, 6 Aug 2026 17:02:04 UTC (277 KB) [v2] Tue, 25 Aug 2026 08:38:51 UTC (277 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: astro-ph.IM < prev | next > new | recent | 2026-08 Change to browse by: astro-ph physics physics.comp-ph References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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