# System identification using Bayesian neural networks with nonparametric noise models

arXiv: https://arxiv.org/abs/2104.12119 · HTML: https://mlsanity.com/paper/2104.12119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 69 references that are in the map.
- First posted on arXiv 25 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Embedding and learning with signatures](https://mlsanity.com/paper/1911.13211/) (2019)
- [Gaussian Process Latent Force Models for Learning and Stochastic Control of Physical Systems](https://mlsanity.com/paper/1709.05409/) (2017)
- [System Identification through Online Sparse Gaussian Process Regression with Input Noise](https://mlsanity.com/paper/1601.08068/) (2016)
- [A Bayesian Nonparametric approach to Reconstruction and Prediction of Random Dynamical Systems](https://mlsanity.com/paper/1511.00154/) (2015)
- [Dependent Mixtures of Geometric Weights Priors](https://mlsanity.com/paper/1701.07776/) (2017)

## Built on by (most cited first, 1 of 1)

- [Neural Harmonium: An Interpretable Deep Structure for Nonlinear Dynamic System Identification with Application to Audio Processing](https://mlsanity.com/paper/2310.07032/) (2023)

## Abstract (arXiv)

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along with its unknown noise processes. In particular, we propose a Bayesian nonparametric approach for system identification in discrete time nonlinear random dynamical systems assuming only the order of the Markov process is known. The proposed method replaces the assumption of Gaussian distributed error components with a highly flexible family of probability density functions based on Bayesian nonparametric priors. Additionally, the functional form of the system is estimated by leveraging Bayesian neural networks which also leads to flexible uncertainty quantification. Asymptotically on the number of hidden neurons, the proposed model converges to full nonparametric Bayesian regression model. A Gibbs sampler for posterior inference is proposed and its effectiveness is illustrated on simulated and real time series.