mlsanityData to 7 Oct 2026

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

arXiv 1902.06278 ↗First posted 17 Feb 2019cs.LG math.DS stat.MLcited by 17

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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.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Feb 2019.

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Citing papers per year: 2021: 8; 2022: 3; 2023: 3; 2024: 1; 2025: 0; 2026: 2.

17 papers.

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  1. 2021Neural graphical modelling in continuous-time: consistency guarantees and algorithmscited by 42
  2. 2021A Probabilistic State Space Model for Joint Inference from Differential Equations and Datacited by 21
  3. 2022AutoIP: A United Framework to Integrate Physics into Gaussian Processescited by 20
  4. 2023Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamicscited by 20
  5. 2024Mechanistic Neural Networks for Scientific Machine Learningcited by 16
  6. 2021Variational multiple shooting for Bayesian ODEs with Gaussian processescited by 15
  7. 2022Fenrir: Physics-Enhanced Regression for Initial Value Problemscited by 11
  8. 2021Pick-and-Mix Information Operators for Probabilistic ODE Solverscited by 6
  9. 2023Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernelscited by 5
  10. 2021Linear-Time Probabilistic Solutions of Boundary Value Problemscited by 1
  11. 2021Distributional Gradient Matching for Learning Uncertain Neural Dynamics Modelscited by 1
  12. 2021Adaptive Low-Pass Filtering using Sliding Window Gaussian Processescited by 1
5 more
  1. 2021MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamicscited by 0
  2. 2022Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equationscited by 0
  3. 2023Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inferencecited by 0
  4. 2026Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processescited by 0
  5. 2026Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systemscited by 0