When Artificial Parameter Evolution Gets Real: Particle Filtering for Time-Varying Parameter Estimation in Deterministic Dynamical Systems

TL;DR

This paper introduces particle filtering algorithms for estimating time-varying parameters in deterministic dynamical systems, addressing challenges of uncertainty quantification from limited data in nonstationary inverse problems.

Contribution

It develops two novel particle filter methods that adaptively estimate parameters and their evolution noise, improving accuracy in nonstationary inverse problems involving ODE models.

Findings

Algorithms accurately estimate various time-varying parameters.

Methods handle different functional forms and relationships with system states.

Demonstrated effectiveness through multiple computational examples.

Abstract

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of these problems includes time-varying parameters with unknown evolution models that often cannot be directly observed. This work develops a systematic particle filtering approach that reframes the idea behind artificial parameter evolution to estimate time-varying parameters in nonstationary inverse problems arising from deterministic dynamical systems. Focusing on systems modeled by ordinary differential equations, we present two particle filter algorithms for time-varying parameter estimation: one that relies on a fixed value for the noise variance of a parameter random walk; another that employs online estimation of the parameter evolution noise variance along with the time-varying parameter of interest. Several computed examples demonstrate the capability of the proposed algorithms in estimating time-varying parameters with different underlying functional forms and different relationships with the system states (i.e., additive vs. multiplicative).