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.