Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins

2026-05-16

AI Summary

This study addresses the challenge of online parameter estimation in digital twins, where low observability, weak excitation, nonlinear dynamics, and biased or noisy measurements hinder accurate inference. To overcome these issues, the authors propose a novel framework that integrates Weighted Flow Matching (WFM) generative modeling with a physics-informed Unscented Kalman Filter (UKF). By dynamically reweighting training samples to emphasize high-information regions of the parameter space, the method enables joint state-parameter estimation that is both data-driven and physically consistent. This work represents the first tight integration of WFM with physics-informed nonlinear filtering, establishing a unified approach for digital twin parameter estimation. Evaluated on spacecraft moment-of-inertia estimation, the proposed method significantly outperforms Extended and Ensemble Kalman Filters under noise and uncertainty, demonstrating superior real-time synchronization capability.

Abstract

Digital twins (DTs) rely on continuous synchronization between physical systems and their virtual counterparts through online parameter estimation under uncertainty. In many practical settings, however, this task is challenged by low observability, weak excitation, nonlinear dynamics, and noisy or biased measurements. In this work, we develop a new mathematical framework that integrates Weighted Flow Matching (WFM) generative modeling with physics-informed nonlinear filtering to enhance parameter estimation in DTs. WFM relies on dynamic reweighting of training samples, which guides the generative model toward parameter regimes most informative of the evolving system state. This generative component is tightly coupled with a physics-informed filtering architecture based on the Unscented Kalman Filter (UKF), yielding a unified DT framework that combines data-driven probability transport with physically consistent state and parameter estimation. The effectiveness of the new integrated framework is demonstrated within a spacecraft DT architecture, where stable moment of inertia estimation is achieved under uncertain and noisy sensing, with significant performance improvements over established approaches such as Extended Kalman Filtering (EKF) and Ensemble Kalman Filtering (EnKF). These results highlight the potential of weighted generative modeling as a core mechanism for real-time DT synchronization in operational and mission-critical systems.

Problem

• Digital Twins
• Parameter Estimation
• Nonlinear Filtering
• Uncertainty
• Online Estimation

Innovation

• Weighted Flow Matching
• Physics-Informed Filtering
• Digital Twins
• Unscented Kalman Filter
• Parameter Estimation