# Deep State Space Models for Nonlinear System Identification

arXiv: https://arxiv.org/abs/2003.14162 · HTML: https://mlsanity.com/paper/2003.14162/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2020.

## Built on by (most cited first, 30 of 30)

- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Deep Subspace Encoders for Nonlinear System Identification](https://mlsanity.com/paper/2210.14816/) (2022)
- [Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty](https://mlsanity.com/paper/2110.08607/) (2021)
- [Sparse Bayesian Deep Learning for Dynamic System Identification](https://mlsanity.com/paper/2107.12910/) (2021)
- [Neural Extended Kalman Filters for Learning and Predicting Dynamics of Structural Systems](https://mlsanity.com/paper/2210.04165/) (2022)
- [OPa-Ma: Text Guided Mamba for 360-degree Image Out-painting](https://mlsanity.com/paper/2407.10923/) (2024)
- [Towards Flexibility and Interpretability of Gaussian Process State-Space Model](https://mlsanity.com/paper/2301.08843/) (2023)
- [Sequential Estimation of Gaussian Process-based Deep State-Space Models](https://mlsanity.com/paper/2301.12528/) (2023)
- [A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data](https://mlsanity.com/paper/2408.02688/) (2024)
- [Stable Linear Subspace Identification: A Machine Learning Approach](https://mlsanity.com/paper/2311.03197/) (2023)
- [Regularization-Based Efficient Continual Learning in Deep State-Space Models](https://mlsanity.com/paper/2403.10123/) (2024)
- [Physics-informed Machine Learning for Calibrating Macroscopic Traffic Flow Models](https://mlsanity.com/paper/2307.06267/) (2023)
- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)
- [Learning Deep Input-Output Stable Dynamics](https://mlsanity.com/paper/2206.13093/) (2022)
- [End-to-End Learning Framework for Solving Non-Markovian Optimal Control](https://mlsanity.com/paper/2502.04649/) (2025)
- [SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems](https://mlsanity.com/paper/2604.14879/) (2026)
- [Non-Autoregressive vs Autoregressive Neural Networks for System Identification](https://mlsanity.com/paper/2105.02027/) (2021)
- [Deep Probabilistic Time Series Forecasting using Augmented Recurrent Input for Dynamic Systems](https://mlsanity.com/paper/2106.05848/) (2021)
- [DeepBayes -- an estimator for parameter estimation in stochastic nonlinear dynamical models](https://mlsanity.com/paper/2205.02264/) (2022)
- [A Variational Autoencoder Framework for Robust, Physics-Informed Cyberattack Recognition in Industrial Cyber-Physical Systems](https://mlsanity.com/paper/2310.06948/) (2023)
- [Data-driven identification of nonlinear dynamical systems with LSTM autoencoders and Normalizing Flows](https://mlsanity.com/paper/2503.03977/) (2025)
- [Switching Recurrent Kalman Networks](https://mlsanity.com/paper/2111.08291/) (2021)
- [Interpretable Latent Variables in Deep State Space Models](https://mlsanity.com/paper/2203.02057/) (2022)
- [Exploiting the capacity of deep networks only at training stage for nonlinear black-box system identification](https://mlsanity.com/paper/2312.15969/) (2023)
- [Recursive Gaussian Process State Space Model](https://mlsanity.com/paper/2411.14679/) (2024)
- [Coordinate ascent neural Kalman-MLE for state estimation](https://mlsanity.com/paper/2511.01855/) (2025)
- [Time-Varying Deep State Space Models for Sequences with Switching Dynamics](https://mlsanity.com/paper/2605.15311/) (2026)
- [Physics-Guided Recurrent State-Space Neural Networks for Multi-Step Prediction](https://mlsanity.com/paper/2606.02278/) (2026)
- [Online Learning via Learned Latent Bayesian Tracking](https://mlsanity.com/paper/2609.31559/) (2026)

## Abstract (arXiv)

Deep state space models (SSMs) are an actively researched model class for temporal models developed in the deep learning community which have a close connection to classic SSMs. The use of deep SSMs as a black-box identification model can describe a wide range of dynamics due to the flexibility of deep neural networks. Additionally, the probabilistic nature of the model class allows the uncertainty of the system to be modelled. In this work a deep SSM class and its parameter learning algorithm are explained in an effort to extend the toolbox of nonlinear identification methods with a deep learning based method. Six recent deep SSMs are evaluated in a first unified implementation on nonlinear system identification benchmarks.