Ensemble Kalman Inversion as an Inertial Interacting Particle System
Abstract
Ensemble Kalman Inversion (EKI) is a derivative-free, ensemble-based method for inverse and optimization problems. A central limitation of its continuous-time dynamics is premature covariance collapse, which can restrict the directions accessible to the inversion and increase sensitivity to the initial ensemble. We introduce a second-order interacting particle system that combines the Kalman force with inertia, damping, attraction towards the ensemble mean, and short-range repulsion. We establish a generalized subspace property showing that nonzero initial velocities may enlarge the affine space accessible to the dynamics, while a finite-ensemble restriction remains. For linear inverse problems, we derive the mean and fluctuation dynamics, identify a regime in which fully collapsed configurations are linearly unstable, characterize asymptotic optimality on the subspace retained by the limiting covariance, and prove exponential decay for the associated frozen-covariance mean dynamics. Numerical experiments on high-dimensional linear and nonlinear inverse problems investigate subspace enlargement, discrepancy-based regularization, and ensemble collapse.
Related
- Polarized Ensemble Kalman Inversion: A Derivative-Free Method for Multimodal Inverse Problems with Non-asymptotic Analysis
- Time-uniform accuracy of ensemble Kalman filters with localization
- Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws
- Large particle number asymptotics for point-interacting bosons in the plane
- Feedback approaches for set-point stabilization of interacting particle systems
BibTeX
@misc{herty2026ensemble,
title = {{Ensemble Kalman Inversion as an Inertial Interacting Particle System}},
author = {Michael Herty and Pierpaolo Porretta and Giuseppe Visconti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.06121},
eprint = {2606.06121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.06121},
}
RIS
TY - UNPB
TI - Ensemble Kalman Inversion as an Inertial Interacting Particle System
AU - Michael Herty
AU - Pierpaolo Porretta
AU - Giuseppe Visconti
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2606.06121
UR - https://arxiv.org/abs/2606.06121
AB - Ensemble Kalman Inversion (EKI) is a derivative-free, ensemble-based method for inverse and optimization problems. A central limitation of its continuous-time dynamics is premature covariance collapse, which can restrict the directions accessible to the inversion and increase sensitivity to the initial ensemble. We introduce a second-order interacting particle system that combines the Kalman force with inertia, damping, attraction towards the ensemble mean, and short-range repulsion. We establish a generalized subspace property showing that nonzero initial velocities may enlarge the affine space accessible to the dynamics, while a finite-ensemble restriction remains. For linear inverse problems, we derive the mean and fluctuation dynamics, identify a regime in which fully collapsed configurations are linearly unstable, characterize asymptotic optimality on the subspace retained by the limiting covariance, and prove exponential decay for the associated frozen-covariance mean dynamics. Numerical experiments on high-dimensional linear and nonlinear inverse problems investigate subspace enlargement, discrepancy-based regularization, and ensemble collapse.
ER -