The article introduces deep Bayesian filtering techniques for nonlinear structural system identification, emphasizing how learnable dynamics can be integrated with physical inductive biases to achieve uncertainty-aware inference. It reviews key models such as the Deep Markov Model, Physics-guided Deep Markov Model, and Neural Extended Kalman Filter, and evaluates them on a three‑dimensional shear‑frame benchmark with hysteretic Bouc‑Wen connections. The study compares measurement‑conditioned reconstruction versus open‑loop forecasting, explores the impact of physical structure on latent‑state interpretability, and discusses robustness in response and parameter estimation, offering practical guidelines for model construction and deployment.
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
arXiv:2607. 20521v1 Announce Type: new Abstract: The state of a dynamic system evolves over time, switching among several latent modes that govern its observable behavior.
arXiv:2602. 23050v2 Announce Type: replace Abstract: Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data.
arXiv:2608. 13621v1 Announce Type: new Abstract: A hidden Markov model (HMM) combines three roles: inference of a hidden-state belief from observations, propagation through a Markov transition, and emission back to observation space.
arXiv:2609.36712v1 Announce Type: cross Abstract: Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this chall...
The paper introduces a new class of algorithms that embed existing automatic differentiation (AD) particle filter methods, enabling a bias‑variance tradeoff and reducing mean squared error in likelihood estimation for partially observed nonlinear stochastic dynamical systems. Unlike prior approaches, these algorithms only require a differentiable simulator of the latent dynamics, not explicit transition probabilities. Numerical experiments demonstrate that a hybrid method—using AD to refine a coarse solution from iterated filtering—outperforms current state‑of‑the‑art techniques on a challenging scientific benchmark.
The paper introduces the Belief Flow Filter (BFF), a generative filtering framework that encodes the evolving posterior distribution directly into flow matching model weights and updates them via test‑time gradient descent. By avoiding particle representations and Gaussian assumptions, BFF aligns structurally with Bayesian filtering and targets the recursive filtering operator. Empirical results on five physical systems—including chaotic dynamics, sparse observations, and a tokamak plasma estimation task—show that BFF outperforms existing methods in most benchmark metrics.
arXiv:2606. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this challenge for stochastic controlled nonlinear dynamical...
arXiv:2607. 05025v1 Announce Type: new Abstract: Vibration-based damage identification in civil infrastructure is a challenging, ill-posed inverse problem due to measurement noise, sparse sensor arrays, and environmental variability.
arXiv:2610.32926v1 Announce Type: new Abstract: State inference and parameter learning for nonlinear filters is a core computation for scientific machine learning with varied applications in engineer...
arXiv:2502.00550v2 Announce Type: replace Abstract: Surrogate models of parametric dynamical systems are essential for many-query and real-time predictions in engineering applications such as design...