PARAMETER AND UNCERTAINTY ESTIMATION FOR DYNAMICAL SYSTEMS USING SURROGATE STOCHASTIC PROCESSES.

Area of Science:

• Dynamical Systems
• Statistical Inference
• Computational Science

Background:

• Inferring unknown quantities in dynamical systems from observational data is crucial for accurate predictions and control.
• Challenges include ill-posed parameter estimation, regularization, prior knowledge incorporation, and computational limits.

Purpose of the Study:

• To develop a new, statistically coherent method for learning parameterized dynamical systems from data.
• To address limitations of conventional approaches in handling complex data features and computational demands.

Main Methods:

• A two-step approach involving fitting a surrogate stochastic process to observational data.
• Utilizing statistical learning to incorporate prior knowledge and handle data features like heteroskedasticity and censoring.
• Employing ordinary point estimation methods on surrogate data samples for modular computation.

Main Results:

• Demonstrated advantages on a predator-prey simulation and within-host influenza virus infection data.
• The proposed method offers modularity and parallelizability.
• Outperformed a conventional Markov chain Monte Carlo (MCMC) based Bayesian approach in real-world applications.

Conclusions:

• The novel two-step method effectively learns parameterized dynamical systems from data.
• This approach provides a robust, computationally efficient, and modular alternative to traditional inference methods.
• Applicable to diverse fields requiring dynamical system modeling from observational data.