mlsanityData to 14 Oct 2026

Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations

arXiv 2306.05566 ↗First posted 8 Jun 2023stat.ML cs.LGcited by 3

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Abstract (arXiv)

Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers indicates that they produce more reliable parameter estimates by better accounting for numerical errors. However, many ODE systems are highly sensitive to their parameter values. This produces deep local maxima in the likelihood function -- a problem which existing probabilistic solvers have yet to resolve. Here we present a novel probabilistic ODE likelihood approximation, DALTON, which can dramatically reduce parameter sensitivity by learning from noisy ODE measurements in a data-adaptive manner. Our approximation scales linearly in both ODE variables and time discretization points, and is applicable to ODEs with both partially-unobserved components and non-Gaussian measurement models. Several examples demonstrate that DALTON produces more accurate parameter estimates via numerical optimization than existing probabilistic ODE solvers, and even in some cases than the exact ODE likelihood itself.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 24 of its 67 references that are in the map. First posted on arXiv 8 Jun 2023.

Builds on

24 of 67 references.

References · 24

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12 more
  1. 2018Convergence Rates of Gaussian ODE Filterscited by 14
  2. 2020Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systemscited by 14
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Citing papers per year: 2024: 2; 2025: 1.

3 papers.

  1. 2024System-Aware Neural ODE Processes for Few-Shot Bayesian Optimizationcited by 3
  2. 2024Adaptive Probabilistic ODE Solvers Without Adaptive Memory Requirementscited by 0
  3. 2025Propagating Model Uncertainty through Filtering-based Probabilistic Numerical ODE Solverscited by 0