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1. Factorization-Based Online Variational Inference for State-Parameter Estimation of Partially Observable Nonlinear Dynamical Systems

   https://doi.org/10.2514/6.2025-1960  

   Wang, Liliang; Gorodetsky, Alex (January 2025, American Institute of Aeronautics and Astronautics)

   We propose an online variational inference framework for joint parameter-state estimation in nonlinear systems. This approach provides a probabilistic estimate of both parameters and states, and does so without relying on a mean-field assumption of independence of the two. The proposed method leverages a factorized form of the target posterior distribution to enable an effective pairing of variational inference for the marginal posterior of parameters with conditional Gaussian filtering for the conditional posterior of the states. This factorization is retrained at every time-step via formulation that combines variational inference and regression. The effectiveness of the framework is demonstrated through applications to two example systems, where it outperforms both the joint Unscented Kalman Filter and Bootstrap Particle Filter parameter-state augmentation in numerical experiments. 

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2. Dynamic Model Identification via Hankel Matrix Fitting: Synchronous Generators and IBRs

   https://doi.org/10.1109/NAPS56150.2022.10012225  

   Alassaf, Abdullah; Fan, Lingling (October 2022, 2022 North American Power Symposium (NAPS))

   This paper presents time-domain measurement data-based dynamic model parameter estimation for synchronous generators and inverter-based resources (IBRs). While prediction error method (PEM) is a well-known and popular method, it requires a good initial guess of parameters which should be in the domain of convergence. Recently, the system identification community has made significant progress in improving the PEM method by taking into consideration of the characteristics of the low-rank data Hankel matrix. In turn, an estimation problem can be formulated as a rank-constraint optimization problem, and further a difference of convex programming (DCP) problem. This paper adopted the data Hankel matrix fitting strategy and developed the problem formulation for the parameter estimation problems for synchronous generators and IBRs. These two examples are presented and the results are satisfying. 

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3. Efficient identification for modeling high-dimensional brain dynamics

   https://doi.org/10.23919/ACC53348.2022.9867232  

   Singh, Matthew F.; Wang, Michael; Cole, Michael W.; Ching, ShiNung (June 2022, 2022 American Control Conference (ACC))

   System identification poses a significant bottleneck to characterizing and controlling complex systems. This challenge is greatest when both the system states and parameters are not directly accessible, leading to a dual-estimation problem. Current approaches to such problems are limited in their ability to scale with many-parameter systems, as often occurs in networks. In the current work, we present a new, computationally efficient approach to treat large dual-estimation problems. In this work, we derive analytic back-propagated gradients for the Prediction Error Method which enables efficient and accurate identification of large systems. The PEM approach consists of directly integrating state estimation into a dual-optimization objective, leaving a differentiable cost/error function only in terms of the unknown system parameters, which we solve using numerical gradient/Hessian methods. Intuitively, this approach consists of solving for the parameters that generate the most accurate state estimator (Extended/Cubature Kalman Filter). We demonstrate that this approach is at least as accurate in state and parameter estimation as joint Kalman Filters (Extended/Unscented/Cubature) and Expectation-Maximization, despite lower complexity. We demonstrate the utility of our approach by inverting anatomically-detailed individualized brain models from human magnetoencephalography (MEG) data. 

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4. Real-time variational method for learning neural trajectory and its dynamics

   Dowling, Matthew; Zhao, Yuan; Park, Il Memming (February 2023, The Eleventh International Conference on Learning Representations)

   Latent variable models have become instrumental in computational neuroscience for reasoning about neural computation. This has fostered the development of powerful offline algorithms for extracting latent neural trajectories from neural recordings. However, despite the potential of real-time alternatives to give immediate feedback to experimentalists, and enhance experimental design, they have received markedly less attention. In this work, we introduce the exponential family variational Kalman filter (eVKF), an online recursive Bayesian method aimed at inferring latent trajectories while simultaneously learning the dynamical system generating them. eVKF works for arbitrary likelihoods and utilizes the constant base measure exponential family to model the latent state stochasticity. We derive a closed-form variational analog to the predict step of the Kalman filter which leads to a provably tighter bound on the ELBO compared to another online variational method. We validate our method on synthetic and real-world data, and, notably, show that it achieves competitive performance. 

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5. Data assimilation for online model calibration in discrete event simulation

   https://doi.org/10.1177/00375497231221578  

   Hu, Xiaolin; Yan, Mingxi (June 2024, SIMULATION)

   The increasing availability of real-time data collected from dynamic systems brings opportunities for simulation models to be calibrated online for improving the accuracy of simulation-based studies. Systematical methods are needed for assimilating real-time measurement data into simulation models. This paper presents a particle filter-based data assimilation method to support online model calibration in discrete event simulation. A joint state-parameter estimation problem is defined, and a particle filter-based data assimilation algorithm is presented. The developed method is applied to a discrete event simulation of a one-way traffic control system. Experiments results demonstrate the effectiveness of the developed method for calibrating simulation models’ parameters in real time and for improving data assimilation results. 

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