PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation
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.
Related
- An Adaptive Online Smoother with Closed-Form Solutions and Information-Theoretic Lag Selection for Conditional Gaussian Nonlinear Systems
- Data assimilation with the 2D Navier–Stokes equations: Optimal Gaussian asymptotics for the posterior measure
- Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data Assimilation
- IEnSF: Iterative ensemble score filter for reducing error in posterior score estimation in nonlinear data assimilation
- On the Nudging Approach to Continuous Data Assimilation in the Limit of Infinite Error Feedback Gain
BibTeX
@misc{tarumi2026prsmoother,
title = {{PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation}},
author = {Yuta Tarumi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26890},
eprint = {2609.26890},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26890},
}
RIS
TY - UNPB
TI - PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation
AU - Yuta Tarumi
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.26890
UR - https://arxiv.org/abs/2609.26890
AB - 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.
ER -