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PR-Smoother advances physical data assimilation by preserving the original simulator while learning non-Gaussian corrections, enabling scalable inference in high-dimensional chaotic systems like Kolmogorov flow. This approach allows joint estimation of states, parameters, and sensor biases directly from observations without replacing underlying dynamics. The method offers a robust framework for handling multimodal posteriors in complex physical models where traditional Gaussian approximations fail.
PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation
arXiv:2609.26890v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD); Atmospheric and Oceanic Physics (physics.ao-ph)
arXiv:2609.26890 [cs.LG]
(or arXiv:2609.26890v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.26890 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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