# Learning Dynamical Systems from Noisy Sensor Measurements using Multiple Shooting

arXiv: https://arxiv.org/abs/2106.11712 · HTML: https://mlsanity.com/paper/2106.11712/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 24 of 24)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [MoCoGAN: Decomposing Motion and Content for Video Generation](https://mlsanity.com/paper/1707.04993/) (2017)
- [Unsupervised Learning of Video Representations using LSTMs](https://mlsanity.com/paper/1502.04681/) (2015)
- [Deep multi-scale video prediction beyond mean square error](https://mlsanity.com/paper/1511.05440/) (2015)
- [Unsupervised Learning for Physical Interaction through Video Prediction](https://mlsanity.com/paper/1605.07157/) (2016)
- [Stochastic Variational Video Prediction](https://mlsanity.com/paper/1710.11252/) (2017)
- [Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Prediction](https://mlsanity.com/paper/2003.01460/) (2020)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Stochastic Adversarial Video Prediction](https://mlsanity.com/paper/1804.01523/) (2018)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [Learning to Decompose and Disentangle Representations for Video Prediction](https://mlsanity.com/paper/1806.04166/) (2018)
- [Video Pixel Networks](https://mlsanity.com/paper/1610.00527/) (2016)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Unsupervised Learning of Object Structure and Dynamics from Videos](https://mlsanity.com/paper/1906.07889/) (2019)
- [Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces](https://mlsanity.com/paper/1905.07357/) (2019)
- [Learning interpretable continuous-time models of latent stochastic dynamical systems](https://mlsanity.com/paper/1902.04420/) (2019)
- [On the smoothness of nonlinear system identification](https://mlsanity.com/paper/1905.00820/) (2019)
- [Curious iLQR: Resolving Uncertainty in Model-based RL](https://mlsanity.com/paper/1904.06786/) (2019)

## Built on by (most cited first, 6 of 6)

- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [Latent Neural ODEs with Sparse Bayesian Multiple Shooting](https://mlsanity.com/paper/2210.03466/) (2022)
- [Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics](https://mlsanity.com/paper/2212.07892/) (2022)
- [Learning Space-Time Continuous Neural PDEs from Partially Observed States](https://mlsanity.com/paper/2307.04110/) (2023)
- [LINOCS: Lookahead Inference of Networked Operators for Continuous Stability](https://mlsanity.com/paper/2404.18267/) (2024)
- [Divide And Conquer: Learning Chaotic Dynamical Systems With Multistep Penalty Neural Ordinary Differential Equations](https://mlsanity.com/paper/2407.00568/) (2024)

## Abstract (arXiv)

Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function approximators such as neural networks to capture the system dynamics directly from sensor measurements. As for now, current methods to learn the parameters of these neural networks are highly sensitive to the inherent instability of most dynamical systems of interest, which in turn prevents the study of very long sequences. In this work, we introduce a generic and scalable method based on multiple shooting to learn latent representations of indirectly observed dynamical systems. We achieve state-of-the-art performances on systems observed directly from raw images. Further, we demonstrate that our method is robust to noisy measurements and can handle complex dynamical systems, such as chaotic ones.