# Green's matching: an efficient approach to parameter estimation in complex dynamic systems

arXiv: https://arxiv.org/abs/2403.14531 · HTML: https://mlsanity.com/paper/2403.14531/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems](https://mlsanity.com/paper/2507.20072/) (2025)

## Abstract (arXiv)

Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green's matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate trajectories in dynamic systems but not their derivatives due to the inverse of differential operators by Green's function. This yields a statistically optimal guarantee for parameter estimation in general-order equations, a feature not shared by existing methods, and provides an efficient framework for broad statistical inferences in complex dynamic systems.