# State estimation with limited sensors -- A deep learning based approach

arXiv: https://arxiv.org/abs/2101.11513 · HTML: https://mlsanity.com/paper/2101.11513/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 59 references that are in the map.
- First posted on arXiv 27 Jan 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Stacked Capsule Autoencoders](https://mlsanity.com/paper/1906.06818/) (2019)
- [Theoretical Analysis of Auto Rate-Tuning by Batch Normalization](https://mlsanity.com/paper/1812.03981/) (2018)
- [Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows](https://mlsanity.com/paper/2007.00936/) (2020)
- [Multi-fidelity Generative Deep Learning Turbulent Flows](https://mlsanity.com/paper/2006.04731/) (2020)
- [Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks](https://mlsanity.com/paper/1807.02901/) (2018)
- [A Gaussian process latent force model for joint input-state estimation in linear structural systems](https://mlsanity.com/paper/1904.00093/) (2019)
- [Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states](https://mlsanity.com/paper/1912.13382/) (2019)
- [Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors](https://mlsanity.com/paper/1902.07358/) (2019)

## Built on by (most cited first, 7 of 7)

- [RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator](https://mlsanity.com/paper/2302.09808/) (2023)
- [A deep learning based surrogate model for stochastic simulators](https://mlsanity.com/paper/2110.13809/) (2021)
- [Machine learning based digital twin for stochastic nonlinear multi-degree of freedom dynamical system](https://mlsanity.com/paper/2103.15636/) (2021)
- [Deep learning fluid flow reconstruction around arbitrary two-dimensional objects from sparse sensors using conformal mappings](https://mlsanity.com/paper/2202.03798/) (2022)
- [EngineBench: Flow Reconstruction in the Transparent Combustion Chamber III Optical Engine](https://mlsanity.com/paper/2406.03325/) (2024)
- [Energy networks for state estimation with random sensors using sparse labels](https://mlsanity.com/paper/2203.06456/) (2022)
- [FR3D: Three-dimensional Flow Reconstruction and Force Estimation for Unsteady Flows Around Extruded Bluff Bodies via Conformal Mapping Aided Convolutional Autoencoders](https://mlsanity.com/paper/2302.01802/) (2023)

## Abstract (arXiv)

The importance of state estimation in fluid mechanics is well-established; it is required for accomplishing several tasks including design/optimization, active control, and future state prediction. A common tactic in this regards is to rely on reduced order models. Such approaches, in general, use measurement data of one-time instance. However, oftentimes data available from sensors is sequential and ignoring it results in information loss. In this paper, we propose a novel deep learning based state estimation framework that learns from sequential data. The proposed model structure consists of the recurrent cell to pass information from different time steps enabling utilization of this information to recover the full state. We illustrate that utilizing sequential data allows for state recovery from only one or two sensors. For efficient recovery of the state, the proposed approached is coupled with an auto-encoder based reduced order model. We illustrate the performance of the proposed approach using two examples and it is found to outperform other alternatives existing in the literature.