Multi-fidelity particle flow filters improve high-dimensional data analysis
Multi-Fidelity Particle Flow Filters based on Log Homotopy
Computational Engineering, Finance, and Science
Summary
When computers try to guess what’s happening inside complex systems, they often use many random samples called particles. But in very detailed problems, these guesses can become unreliable and slow. The authors created a new method that mixes a few accurate but costly guesses with lots of cheaper, simpler ones to make better predictions faster. They tested their idea on fluid and wave problems and got results just as good as the expensive methods but at much lower cost.
What this means in practice
- •For weather modelers: Run weather prediction models combining detailed simulations with simplified versions to achieve accuracy with less computing time.
- •For computational fluid engineers: Improve flow state estimation by integrating high- and low-resolution simulation data efficiently to reduce simulation costs.
Authors
Abhinab Bhattacharjee, Andrey A. Popov, Amit N. Subrahmanya, Adrian Sandu
Abstract
This work proposes a new Multi-Fidelity Particle Flow Filter (MFPFF) based on a linear control variate framework and multilevel Monte Carlo methods. Conventional particle filters often suffer from weight collapse and particle degeneracy in high-dimensional spaces. Particle flow filters address this by smoothly transporting prior particles toward the posterior distribution, thereby avoiding the need for resampling. This work constructs multi-fidelity particle flow filters by augmenting a small number of expensive high-fidelity particles (full-order model runs) with a large number of inexpensive low-resolution particles (reduced-order surrogates constructed via intrusive Galerkin projection). These surrogates act as control variates to enhance the statistical estimate of the full-order posterior, yielding enhanced analysis accuracy at comparable computational cost. The work focuses on two particle flows based on log homotopy, the stochastic Gromov flow and deterministic Exact flow. Numerical experiments with the Korteweg-De Vries (KdV) and Quasi-Geostrophic (QG) test problems demonstrate that the proposed MFPFF achieves accuracy comparable to high-fidelity simulations while significantly reducing computational expense.