Statistical inference in mechanistic models: time warping for improved gradient matching

Mu Niu, Benn Macdonald, Simon Rogers, Maurizio Filippone, Dirk Husmeier*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios.

Original languageEnglish (US)
Pages (from-to)1091-1123
Number of pages33
JournalComputational Statistics
Issue number2
StatePublished - Jun 1 2018


  • Differential equations
  • Dynamical systems
  • Objective function
  • Reproducing kernel Hilbert space

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics


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