[Submitted on 22 Sep 2026]
Title:PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation
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Abstract:Many physical data assimilation (DA) workflows require smoothing methods that represent non-Gaussian posteriors over physical state variables, scale to high-dimensional simulators, train from observation windows alone, and remain compatible with calibration of the prescribed simulator. We introduce PR-Smoother, a simulator-preserving amortized smoother designed for this prescribed-simulator DA regime. Its key design principle is to keep the prescribed simulator explicit in both the evidence lower bound and the variational family: rather than learning replacement dynamics or a learned trajectory prior, PR-Smoother learns only future-conditioned corrections around the prescribed rollout. This yields an explicit non-Gaussian smoothing distribution over physical trajectories and supports joint state, parameter, and sensor-bias learning from observations alone. The variational family contains the exact smoother in deterministic and linear-Gaussian limits. Empirically, PR-Smoother captures multimodal posteriors in 4-dimensional Lorenz-96, remains accurate under ambiguous nonlinear observations and process noise in 40-dimensional Lorenz-96, and scales to joint state-parameter-bias inference in 16,384-dimensional Kolmogorov flow.
Subjects:
Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD); Atmospheric and Oceanic Physics (physics.ao-ph)
Report number: RIKEN-iTHEMS-Report-26
Cite as: arXiv:2609.26890 [cs.LG]
(or arXiv:2609.26890v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.26890
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Yuta Tarumi [view email] [v1] Tue, 22 Sep 2026 18:00:06 UTC (4,398 KB)
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