arXiv Statistics ML By Wei Liu, Konstantinos Vlachas, Eleni Chatzi

Deep Bayesian Approaches for Interpretable Nonlinear Structural System Identification

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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.

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arXiv Statistics ML
Oct 23

Automatic Differentiation for Inference on Partially Observed Markov Process Models

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.

By Kevin Tan, Aaron J. Abkemeier, Kunyang He, Giles Hooker, Edward L. Ionides