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

• URL: http://arxiv.org/abs/2605.17146v1
• Date: Sat, 16 May 2026 20:31:29 GMT
• Title: Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins
• Abstract summary: Digital twins (DTs) rely on continuous synchronization between physical systems and their virtual counterparts.<n>We develop a new mathematical framework that integrates Weighted Flow Matching (WFM) generative modeling with physics-informed nonlinear filtering.
• Score: 2.5967371714399787
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• SNM-VFI: Symmetric Nonlinear Motion-Guided Generative Video Frame Interpolation [54.26896703895789]
  We propose a training-free framework for motion-controllable generative video frames with pre-trained optical flow and video diffusion models.<n>SNM-VFI achieves strong perceptual quality, competitive reconstruction accuracy, and robust temporal coherence across diverse motion scenarios.
  arXiv  Detail & Related papers  (2026-08-13T16:43:49Z)
• The Kerimov-Alekberli Model: An Information-Geometric Framework for Real-Time System Stability [0.0]
  This study introduces the Kerimov-Alekberli model, a novel information-geometric framework that redefines AI safety.<n>By formally linking non-equilibrium thermodynamics to control for the ethical alignment of autonomous systems, we define systemic anomalies.<n> Validation on the NSL-KDD dataset and unmanned aerial vehicle trajectory simulations demonstrated that our model achieves effective real-time detection.
  arXiv  Detail & Related papers  (2026-04-27T06:13:25Z)
• Online Inertia Tensor Identification for Non-Cooperative Spacecraft via Augmented UKF [0.0]
  This paper presents an augmented Unscented Kalman Filter (UKF) framework designed to jointly estimate the relative 6-DOF pose and the full inertia tensor of a non-cooperative target spacecraft.<n>The proposed architecture fuses visual measurements from monocular vision-based Convolutional Neural Networks (CNN) with depth information from LiDAR to constrain the coupled rigid-body dynamics.<n>By augmenting the state vector to include the six independent elements of the inertia tensor, the filter dynamically recovers the target's normalized mass distribution in real-time without requiring ground-based pre-calibration.
  arXiv  Detail & Related papers  (2026-03-28T18:13:03Z)
• Is Flow Matching Just Trajectory Replay for Sequential Data? [46.770624059457724]
  Flow matching (FM) is increasingly used for time-series generation.<n>It is not well understood whether it learns a general dynamical structure or simply performs an effective "trajectory replay"<n>We show that the implied sampler is an ODE whose dynamics constitutes a nonparametric, memory-augmented continuous-time dynamical system.
  arXiv  Detail & Related papers  (2026-02-09T06:48:45Z)
• Fractional-order Modeling for Nonlinear Soft Actuators via Particle Swarm Optimization [49.34452620841728]
  This paper proposes an innovative modeling framework based on fractional-order differential equations (FODEs) to capture the dynamic behavior of soft materials.<n>The proposed approach effectively represents the complex deformation phenomena inherent in soft actuators.
  arXiv  Detail & Related papers  (2025-12-20T04:46:25Z)
• Model-Based Diffusion Sampling for Predictive Control in Offline Decision Making [48.998030470623384]
  offline decision-making requires reliable behaviors from fixed datasets without further interaction.<n>We propose a compositional model-based diffusion framework consisting of: (i) a planner that generates diverse, task-aligned trajectories; (ii) a dynamics model that enforces consistency with the underlying system dynamics; and (iii) a ranker module that selects behaviors aligned with the task objectives.
  arXiv  Detail & Related papers  (2025-12-09T06:26:02Z)
• On-line learning of dynamic systems: sparse regression meets Kalman filtering [41.99844472131922]
  We extend sparsity-driven approaches to real-time learning by integrating a cornerstone algorithm from control theory -- the Kalman filter (KF)<n>The resulting Sindy Kalman Filter (KF) unifies both frameworks by treating unknown system parameters as state variables.<n>We demonstrate KF's effectiveness in the real-time identification of a sparse nonlinear aircraft model built from real flight data.
  arXiv  Detail & Related papers  (2025-11-14T11:24:05Z)
• Flow marching for a generative PDE foundation model [0.0]
  We propose Flow Marching, an algorithm that bridges neural operator learning with flow matching motivated by an analysis of error accumulation in physical dynamical systems.<n>We also introduce a Physics-Pretrained Variational Autoencoder (P2E) to embed physical trajectories into a compact latent space.<n>We curate a corpus of 2.5M trajectories across 12 distinct PDE families and train suites of P2Es and FMTs at multiple scales.
  arXiv  Detail & Related papers  (2025-09-23T04:00:41Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Fine-Tuning Hybrid Physics-Informed Neural Networks for Vehicle Dynamics Model Estimation [2.432448600920501]
  This paper introduces the Fine-Tuning Hybrid Dynamics (FTHD) method, which integrates supervised and unsupervised Physics-Informed Neural Networks (PINNs) FTHD fine-tunes a pre-trained Deep Dynamics Model (DDM) using a smaller training dataset, delivering superior performance compared to state-of-the-art methods. An Extended Kalman Filter (EKF) is embedded within FTHD to effectively manage noisy real-world data, ensuring accurate denoising. Results demonstrate that the hybrid approach significantly improves parameter estimation accuracy, even with reduced data, and outperforms existing models.
  arXiv  Detail & Related papers  (2024-09-29T10:33:07Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.