Physical Parameter Estimation via Ensemble Kalman Filtering

In this project, we study joint state and parameter estimation in nonlinear dynamical systems observed through noisy, partial measurements. We examine three approaches within the Ensemble Kalman Filter (EnKF) framework: a naive gradient method, a state-augmented EnKF, and an autodifferentiated EnKF (AD-EnKF) that backpropagates through the full filtering computation graph to capture the complete gradient of the data log-likelihood.

Methods are benchmarked on the Lorenz 63 system—a canonical chaotic attractor—and extended to a high-dimensional generalized Lotka–Volterra ecological system with 5 species and 20 unknown parameters. We compare AD-EnKF against the Iterated Ensemble Kalman Smoother (IEnKS), finding that the smoother’s access to bidirectional temporal information allows it to recover all 20 ecosystem parameters with high precision, resolving the fundamental limitation of causal filtering on slow-timescale dynamics. For a full treatment of the methods and results, see the project report.