The authors introduce implicit data assimilation, defining the analysis law as an energy tilt of the forecast distribution to handle observation mechanisms that are many-to-one, implicit, or non-smooth. They propose the Ensemble Controlled-flow Filter (EnCF), which realizes this update through a stochastic controlled flow and learns the observation-dependent control by adjoint matching from terminal energy gradients.
- EnCF-LF learns a surrogate conditional energy from samples for simulator-defined observations.
- The paper proves ideal exactness, derives a one-step error decomposition, and establishes non-accumulation of local errors under filter stability.
- Numerical results indicate that while Kalman-type filters remain preferable for smooth additive-Gaussian observations, EnCF is better suited to non-Gaussian, many-to-one, multimodal, and implicit observation models.
This approach provides a viable alternative for data assimilation scenarios where existing ensemble filters fail due to the lack of residual structures or likelihood guidance.