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

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.
• 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.