# Reproducing kernel Hilbert space based estimation of systems of ordinary differential equations

arXiv: https://arxiv.org/abs/1311.3576 · HTML: https://mlsanity.com/paper/1311.3576/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2013.

## Built on by (most cited first, 5 of 5)

- [Experimental Design for Linear Functionals in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.13627/) (2022)
- [Post-Regularization Confidence Bands for Ordinary Differential Equations](https://mlsanity.com/paper/2110.12510/) (2021)
- [MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamics](https://mlsanity.com/paper/2105.12894/) (2021)
- [Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations](https://mlsanity.com/paper/2202.12932/) (2022)
- [Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference](https://mlsanity.com/paper/2307.00032/) (2023)

## Abstract (arXiv)

Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models in many branches of science they have not been the focus of systematic statistical analysis until recently. In this work we propose a general approach to estimate the parameters of systems of differential equations measured with noise. Our methodology is based on the maximization of the penalized likelihood where the system of differential equations is used as a penalty. To do so, we use a Reproducing Kernel Hilbert Space approach that allows to formulate the estimation problem as an unconstrained numeric maximization problem easy to solve. The proposed method is tested with synthetically simulated data and it is used to estimate the unobserved transcription factor CdaR in Steptomyes coelicolor using gene expression data of the genes it regulates.