Reduced-Order Autodifferentiable Ensemble Kalman Filters
This work addresses surrogate state reconstruction and forecasting for computational efficiency in dynamical systems, representing an incremental improvement over existing methods.
The paper tackles the problem of reconstructing and forecasting partially observed states from unknown or expensive dynamical systems by introducing ROAD-EnKFs, which learn a low-dimensional surrogate model and decoder for use in an ensemble Kalman filter, achieving higher accuracy at lower computational cost when low-dimensional structure exists and similar accuracy at lower cost otherwise.
This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman filters (ROAD-EnKFs) learn a latent low-dimensional surrogate model for the dynamics and a decoder that maps from the latent space to the state space. The learned dynamics and decoder are then used within an ensemble Kalman filter to reconstruct and forecast the state. Numerical experiments show that if the state dynamics exhibit a hidden low-dimensional structure, ROAD-EnKFs achieve higher accuracy at lower computational cost compared to existing methods. If such structure is not expressed in the latent state dynamics, ROAD-EnKFs achieve similar accuracy at lower cost, making them a promising approach for surrogate state reconstruction and forecasting.