Parameter and uncertainty estimation for dynamical systems using surrogate stochastic processes

Matthias Chung, Mickael Binois, Robert B. Gramacy, Johnathan M. Bardsley, David J. Moquin, Amanda P. Smith, Amber Smith

Research output: Contribution to journalArticle

Abstract

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging mathematical theory with empirical measurements in a statistically coherent way is critical and challenges abound, e.g., ill-posedness of the parameter estimation problem, proper regularization and incorporation of prior knowledge, and computational limitations. To address these issues, we propose a new method for learning pa-rameterized dynamical systems from data. We first customize and fit a surrogate stochastic process directly to observational data, front-loading with statistical learning to respect prior knowledge (e.g., smoothness), cope with challenging data features like heteroskedasticity, heavy tails, and censoring. Then, samples of the stochastic process are used as ``surrogate data"" and point estimates are computed via ordinary point estimation methods in a modular fashion. Attractive features of this two-step approach include modularity and trivial parallelizability. We demonstrate its advantages on a predator-prey simulation study and on a real-world application involving within-host influenza virus infection data paired with a viral kinetic model, with comparisons to a more conventional Markov chain Monte Carlo (MCMC) based Bayesian approach.

Original languageEnglish (US)
Pages (from-to)A2212-A2238
JournalSIAM Journal on Scientific Computing
Volume41
Issue number4
DOIs
StatePublished - Jan 1 2019

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Uncertainty Estimation
Random processes
Parameter Estimation
Stochastic Processes
Dynamical systems
Dynamical system
Robust control
Viruses
Prior Knowledge
Merging
Parameter estimation
Markov processes
Paired Data
Surrogate Data
Heteroskedasticity
Statistical Learning
Point Estimation
Kinetics
Ill-posedness
Heavy Tails

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

Parameter and uncertainty estimation for dynamical systems using surrogate stochastic processes. / Chung, Matthias; Binois, Mickael; Gramacy, Robert B.; Bardsley, Johnathan M.; Moquin, David J.; Smith, Amanda P.; Smith, Amber.

In: SIAM Journal on Scientific Computing, Vol. 41, No. 4, 01.01.2019, p. A2212-A2238.

Research output: Contribution to journalArticle

Chung, Matthias ; Binois, Mickael ; Gramacy, Robert B. ; Bardsley, Johnathan M. ; Moquin, David J. ; Smith, Amanda P. ; Smith, Amber. / Parameter and uncertainty estimation for dynamical systems using surrogate stochastic processes. In: SIAM Journal on Scientific Computing. 2019 ; Vol. 41, No. 4. pp. A2212-A2238.
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