# Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs

arXiv: https://arxiv.org/abs/1804.04378 · HTML: https://mlsanity.com/paper/1804.04378/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2018.

## Built on by (most cited first, 17 of 17)

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- [Exact Inference for Continuous-Time Gaussian Process Dynamics](https://mlsanity.com/paper/2309.02351/) (2023)
- [Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks](https://mlsanity.com/paper/2302.07260/) (2023)
- [Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models](https://mlsanity.com/paper/2106.11609/) (2021)
- [Approximate Latent Force Model Inference](https://mlsanity.com/paper/2109.11851/) (2021)
- [MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamics](https://mlsanity.com/paper/2105.12894/) (2021)
- [Using Intermediate Forward Iterates for Intermediate Generator Optimization](https://mlsanity.com/paper/2302.02336/) (2023)
- [Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference](https://mlsanity.com/paper/2307.00032/) (2023)
- [Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model](https://mlsanity.com/paper/2507.10884/) (2025)
- [Gaussian process learning with flow map refinement for parameter estimation in dynamical systems](https://mlsanity.com/paper/2608.22324/) (2026)

## Abstract (arXiv)

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computational cost are well established, a rigorous mathematical framework has been missing. We offer a novel interpretation which leads to a better understanding and improvements in state-of-the-art performance in terms of accuracy for nonlinear dynamical systems.