Aug 2026· International Journal of Network Dynamics and Intelligence· Vol 5· 0 citations· 38 references
TL;DR
A deep variational identification method for nonlinear state-space models based on a structured Gaussian posterior using a non-causal dilated residual convolutional network and a Markov structure with block-tridiagonal precision is proposed to ensure linear-time inference.
Abstract
Nonlinear state-space model identification is inherently challenging due to the need for joint latent-state inference and parameter learning. Variational inference offers a tractable framework, where structured Gaussian posteriors enable scalable inference over latent trajectories. However, existing parameterizations of the posterior mean struggle to capture complex nonlinear dynamics, while more expressive deep parameterizations tend to introduce instability in joint optimization. To address these issues, this article proposes a deep variational identification method for nonlinear state-space models based on a structured Gaussian posterior. Specifically, the posterior mean is parameterized using a non-causal dilated residual convolutional network, while a Markov structure with block-tridiagonal precision is preserved to ensure linear-time inference. Furthermore, an alternating optimization scheme is developed to separate variational smoothing from model identification. The variational parameters are updated by maximizing a differentiable approximation to the evidence lower bound, whereas the model and noise parameters are updated via analytic identification steps using samples from the variational posterior. Experiments on a nonlinear discrete-time system and a stochastic Duffing oscillator demonstrate that the proposed approach achieves stable optimization and reliable estimation of the system dynamics and noise statistics.
This work proposes a fully probabilistic extension of the manifold meta-learning framework, based on amortized Variational Inference, where a generative prior over the low-dimensional parameter manifold is learned.
Matteo Rufolo, D. Piga, M. Forgione· arXiv.org· 0 citations
A physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation and the robustness of the proposed framework is demonstrated, which generally reduces calibration error and variability compared with the standard surrogate models.
Qiyao Zhou, Xujia Zhu, Pierre Joli et al.· 0 citations
We propose a filtering-oriented end-to-end learning framework to identify reduced-order models explicitly tailored for state estimation in high-dimensional nonlinear systems. An autoencoder (AE) neural network learns a low-dimensional latent representation of the state together with a lifting map to the original space, while a reduced-order linear time-invariant (RO-LTI) model describes the latent dynamics. The AE and RO-LTI model are trained jointly by minimizing a multi-objective loss that combines reconstruction error with a filtering objective based on a differentiable Kalman filter, ensuring that the reduced-order model is tailored for the downstream state estimation task. At inference, filtering is performed entirely in the latent space using the RO-LTI model, and the estimated state is mapped back to the original space via the decoder. Unlike conventional two-stage approaches, in which a reduced-order model is first identified for system approximation and a filter is subsequently designed on top of it, the proposed framework learns a task-oriented reduced-order model whose parameters are shaped entirely by filtering performance rather than system approximation accuracy alone. We further quantify probabilistic bounds on the performance gap between full-order and reduced-order filters using conformal predictions, which do not require assumption on data distribution. The approach is validated on a heat diffusion benchmark, where the full temperature field is reconstructed from sparse measurements.
Manas Mejari, M. B. Dehkordi, D. Piga· arXiv.org· 0 citations
This work first learns an implicit spectral predictor using Observation Spectral Filtering using Observation Spectral Filtering, a convex method that competes with the best linear observer for the system, and applies spectral-to-LDS distillation to convert this predictor into an explicit recurrent linear dynamical system.
Liane Galanti, Devan Shah, Shlomo Fortgang et al.· 0 citations
This paper develops an online, off-policy policy-iteration framework for reinforcement learning (RL), based on sparse Gaussian-mixture-model Q-functions (S-GMM-QFs). The framework reconciles streaming, non-stationary data with the Riemannian structure of the parameter space while handling distributional mismatch through experience replay. S-GMM-QFs are introduced via Hadamard overparametrization, enabling interpretable sparsification through smooth regularization that facilitates Riemannian-based optimization. Overparametrization allows the framework to adaptively identify meaningful components from a large initial pool, yielding sparse models where interpretability emerges naturally from geometry: each component's parameters (means and covariances) explicitly encode its geometric role in the ambient state-action space. These geometric roles are learned through online gradient descent on a smooth objective over a (Cartesian-product) Riemannian manifold. Numerical tests demonstrate that S-GMM-QFs match or exceed deep RL methods while using substantially fewer parameters and achieving faster improvement per observed transition. Notably, parameter efficiency and interpretability combine to maintain strong generalization in low-parameter regimes where sparsified deep RL approaches degrade.
