# ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systems

arXiv: https://arxiv.org/abs/1902.06278 · HTML: https://mlsanity.com/paper/1902.06278/

## Key facts

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

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

- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [A Probabilistic State Space Model for Joint Inference from Differential Equations and Data](https://mlsanity.com/paper/2103.10153/) (2021)
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- [Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics](https://mlsanity.com/paper/2302.13271/) (2023)
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- [Fenrir: Physics-Enhanced Regression for Initial Value Problems](https://mlsanity.com/paper/2202.01287/) (2022)
- [Pick-and-Mix Information Operators for Probabilistic ODE Solvers](https://mlsanity.com/paper/2110.10770/) (2021)
- [Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels](https://mlsanity.com/paper/2310.05387/) (2023)
- [Linear-Time Probabilistic Solutions of Boundary Value Problems](https://mlsanity.com/paper/2106.07761/) (2021)
- [Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models](https://mlsanity.com/paper/2106.11609/) (2021)
- [Adaptive Low-Pass Filtering using Sliding Window Gaussian Processes](https://mlsanity.com/paper/2111.03617/) (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)
- [Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes](https://mlsanity.com/paper/2605.13088/) (2026)
- [Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systems](https://mlsanity.com/paper/2609.37944/) (2026)

## Abstract (arXiv)

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian processes and leverage it to build a computationally and data efficient algorithm for state and parameter inference. In an extensive set of experiments, our approach outperforms the current state of the art for parameter inference both in terms of accuracy and computational cost. It also shows promising results for the much more challenging problem of model selection.