# Ensemble Kalman Methods With Constraints

arXiv: https://arxiv.org/abs/1901.05668 · HTML: https://mlsanity.com/paper/1901.05668/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [Neural Dynamical Operator: Continuous Spatial-Temporal Model with Gradient-Based and Derivative-Free Optimization Methods](https://mlsanity.com/paper/2311.11798/) (2023)
- [Learning About Structural Errors in Models of Complex Dynamical Systems](https://mlsanity.com/paper/2401.00035/) (2023)
- [Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods](https://mlsanity.com/paper/2104.03384/) (2021)
- [Preserving linear invariants in ensemble filtering methods](https://mlsanity.com/paper/2404.14328/) (2024)
- [Online optimisation for dynamic electrical impedance tomography](https://mlsanity.com/paper/2412.12944/) (2024)
- [Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems](https://mlsanity.com/paper/2504.13320/) (2025)

## Abstract (arXiv)

Ensemble Kalman methods constitute an increasingly important tool in both state and parameter estimation problems. Their popularity stems from the derivative-free nature of the methodology which may be readily applied when computer code is available for the underlying state-space dynamics (for state estimation) or for the parameter-to-observable map (for parameter estimation). There are many applications in which it is desirable to enforce prior information in the form of equality or inequality constraints on the state or parameter. This paper establishes a general framework for doing so, describing a widely applicable methodology, a theory which justifies the methodology, and a set of numerical experiments exemplifying it.