Nonlinear structural system identification remains challenging when governing physics is only partially known and measurements are sparse. Deep Bayesian filtering addresses these challenges by combining learnable dynamical representations with probabilistic state-space models, physical inductive biases, and uncertainty-aware inference. This paper presents, for the first time, a unified tutorial treatment of deep Bayesian filtering for nonlinear structural system identification, connecting model formulation, learning, posterior inference, and evaluation. Amortized variational inference and differentiable Kalman filtering are introduced as complementary strategies within this broader framework. The Deep Markov Model (DMM) provides a data-driven reference, while the Physics-guided Deep Markov Model (PgDMM) and Neural Extended Kalman Filter (Neural EKF) serve as illustrative instances through which methodological choices and their implications are examined. Dynamic state estimation and joint state and parameter estimation are demonstrated on a three-dimensional shear-frame benchmark with hysteretic Bouc-Wen connections and sparse acceleration measurements. The comparative analysis yields new observations concerning the relationships among reconstruction accuracy, predictive fidelity, physical interpretability, and estimation robustness. Physical structure improves latent-state interpretability without necessarily ensuring faithful predictive dynamics, while comparable typical reconstruction accuracy can conceal substantial differences in estimation robustness. These findings motivate practical guidelines for model construction, training, and evaluation that distinguish reconstruction, forecasting, state recovery, and parameter identification. The tutorial concludes by outlining challenges in uncertainty calibration, identifiability, and validation on real structures.
Many computational models exhibit multiple operating regimes separated by abrupt or non-smooth transitions as the input parameters vary. Such regime transitions complicate the construction of global parametric reduced-order models, often necessitating large training datasets to capture the distinct system behaviors. Accurate regime boundary detection instead enables localized modeling strategies by partitioning the parameter space into regions of qualitatively distinct behavior. In many cases, regime switching corresponds to the excursion set of a simulator output. When such a quantity is discontinuous or non-smooth, regression-based algorithms for level set estimation can struggle to correctly approximate the boundary. In this work, we show that solving a resulting binary classification problem can improve sample efficiency and we further propose a novel adaptive sampling strategy for support vector machines. Unlike uncertainty-based sampling schemes, the proposed approach uses a continuous search space and efficiently explores the currently estimated boundary in its tangential directions by gradient-based dynamic sampling. Because the decision function admits analytical gradients, this exploration incurs negligible computational overhead relative to the underlying model evaluations. Then, a space-filling subset of the generated samples is selected as the next batch to be queried. We demonstrate improved sample efficiency compared to existing active learning algorithms on analytical and numerical examples. The proposed method provides a sample-efficient framework for regime boundary detection in a broad class of discontinuous simulation-driven problems.