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Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes.

Shihao Yang1, Samuel W K Wong2, S C Kou3

  • 1H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332.

Proceedings of the National Academy of Sciences of the United States of America
|April 10, 2021
PubMed
Summary
This summary is machine-generated.

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We introduce manifold-constrained Gaussian process inference (MAGI), a fast and accurate Bayesian method for estimating parameters in nonlinear dynamic systems. MAGI efficiently models time series data, even with unobserved components, by constraining Gaussian processes to satisfy ordinary differential equations.

Area of Science:

  • Computational Science
  • Statistical Modeling
  • Dynamical Systems

Background:

  • Parameter estimation for nonlinear dynamic systems is crucial across scientific disciplines.
  • Existing methods often struggle with noisy, sparse data and computational demands.
  • Unobserved system components present a significant challenge in real-world experimental data.

Purpose of the Study:

  • To develop a fast and accurate Bayesian inference method for nonlinear dynamic systems.
  • To address challenges posed by noisy, sparse data and unobserved components.
  • To bypass computationally intensive numerical integration in parameter estimation.

Main Methods:

  • Manifold-constrained Gaussian process inference (MAGI) is proposed.
  • A Gaussian process model is conditioned on ordinary differential equations (ODEs) via a manifold constraint.
Keywords:
inverse problemordinary differential equationsparameter estimationposterior sampling

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  • This approach avoids numerical integration, enabling significant computational savings.

    • Main Results:

    • MAGI demonstrates high accuracy and speed in parameter estimation.
    • The method effectively handles time series data with unobserved system components.
    • Performance is validated using realistic physical experiment examples.

    Conclusions:

    • MAGI offers a principled Bayesian framework for nonlinear dynamic system modeling.
    • The manifold constraint provides a statistically robust way to incorporate ODEs.
    • MAGI represents a significant advancement in efficient and accurate parameter estimation for dynamic systems.