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

arXiv: https://arxiv.org/abs/2204.00074 · HTML: https://mlsanity.com/paper/2204.00074/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2022.

## Built on by (most cited first, 2 of 2)

- [Parameter inference from a non-stationary unknown process](https://mlsanity.com/paper/2407.08987/) (2024)
- [Dynamics-Encoded Deep Learning for Robust System Identification and Parameter Estimation](https://mlsanity.com/paper/2410.04299/) (2024)

## Abstract (arXiv)

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).