# dynoGP: Deep Gaussian Processes for dynamic system identification

arXiv: https://arxiv.org/abs/2502.05620 · HTML: https://mlsanity.com/paper/2502.05620/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 8 Feb 2025.

## Builds on (most cited first, 17 of 17)

- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [dynoNet: a neural network architecture for learning dynamical systems](https://mlsanity.com/paper/2006.02250/) (2020)
- [Deep Sigma Point Processes](https://mlsanity.com/paper/2002.09112/) (2020)
- [Model structures and fitting criteria for system identification with neural networks](https://mlsanity.com/paper/1911.13034/) (2019)
- [Time series forecasting with Gaussian Processes needs priors](https://mlsanity.com/paper/2009.08102/) (2020)
- [Baseline Results for Selected Nonlinear System Identification Benchmarks](https://mlsanity.com/paper/2405.10779/) (2024)
- [Correlated Product of Experts for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2112.09519/) (2021)

## Built on by (most cited first, 3 of 3)

- [Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification](https://mlsanity.com/paper/2510.24757/) (2025)
- [xFODE: An Explainable Fuzzy Additive ODE Framework for System Identification](https://mlsanity.com/paper/2604.14883/) (2026)
- [Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2605.11460/) (2026)

## Abstract (arXiv)

In this work, we present a novel approach to system identification for dynamical systems, based on a specific class of Deep Gaussian Processes (Deep GPs). These models are constructed by interconnecting linear dynamic GPs (equivalent to stochastic linear time-invariant dynamical systems) and static GPs (to model static nonlinearities). Our approach combines the strengths of data-driven methods, such as those based on neural network architectures, with the ability to output a probability distribution. This offers a more comprehensive framework for system identification that includes uncertainty quantification. Using both simulated and real-world data, we demonstrate the effectiveness of the proposed approach.