# Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction

arXiv: https://arxiv.org/abs/2307.11793 · HTML: https://mlsanity.com/paper/2307.11793/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 70 references that are in the map.
- First posted on arXiv 20 Jul 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Recurrent Neural Network Regularization](https://mlsanity.com/paper/1409.2329/) (2014)
- [Recent Advances in Recurrent Neural Networks](https://mlsanity.com/paper/1801.01078/) (2017)
- [Data-Driven Sparse Sensor Placement for Reconstruction](https://mlsanity.com/paper/1701.07569/) (2017)
- [Data Assimilation: A Mathematical Introduction](https://mlsanity.com/paper/1506.07825/) (2015)
- [Learning Efficient Navigation in Vortical Flow Fields](https://mlsanity.com/paper/2102.10536/) (2021)
- [Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using Reinforcement Learning](https://mlsanity.com/paper/1907.08591/) (2019)
- [Optimal control of point-to-point navigation in turbulent time-dependent flows using Reinforcement Learning](https://mlsanity.com/paper/2103.00329/) (2021)
- [Finite-Horizon, Energy-Optimal Trajectories in Unsteady Flows](https://mlsanity.com/paper/2103.10556/) (2021)
- [Dynamic Compressed Sensing of Unsteady Flows with a Mobile Robot](https://mlsanity.com/paper/2110.08658/) (2021)
- [Mobile Sensor Path Planning for Kalman Filter Spatiotemporal Estimation](https://mlsanity.com/paper/2212.08280/) (2022)

## Built on by (most cited first, 12 of 12)

- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2501.13329/) (2025)
- [Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics](https://mlsanity.com/paper/2405.11955/) (2024)
- [From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility](https://mlsanity.com/paper/2503.08907/) (2025)
- [Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2503.08904/) (2025)
- [Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspective](https://mlsanity.com/paper/2409.02349/) (2024)
- [T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoders](https://mlsanity.com/paper/2506.15881/) (2025)
- [Constrained Sensing and Reliable State Estimation with Shallow Recurrent Decoders on a TRIGA Mark II Reactor](https://mlsanity.com/paper/2510.12368/) (2025)
- [CS-SHRED: Enhancing SHRED for Robust Recovery of Spatiotemporal Dynamics](https://mlsanity.com/paper/2507.22303/) (2025)
- [Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applications](https://mlsanity.com/paper/2606.05202/) (2026)
- [Real-time optimal control with shallow recurrent decoder networks](https://mlsanity.com/paper/2607.19302/) (2026)
- [Real-Time Monitoring of MHD Liquid Metal Flows with Shallow Recurrent Decoders](https://mlsanity.com/paper/2608.28366/) (2026)

## Abstract (arXiv)

Sensing is one of the most fundamental tasks for the monitoring, forecasting and control of complex, spatio-temporal systems. In many applications, a limited number of sensors are mobile and move with the dynamics, with examples including wearable technology, ocean monitoring buoys, and weather balloons. In these dynamic systems (without regions of statistical-independence), the measurement time history encodes a significant amount of information that can be extracted for critical tasks. Most model-free sensing paradigms aim to map current sparse sensor measurements to the high-dimensional state space, ignoring the time-history all together. Using modern deep learning architectures, we show that a sequence-to-vector model, such as an LSTM (long, short-term memory) network, with a decoder network, dynamic trajectory information can be mapped to full state-space estimates. Indeed, we demonstrate that by leveraging mobile sensor trajectories with shallow recurrent decoder networks, we can train the network (i) to accurately reconstruct the full state space using arbitrary dynamical trajectories of the sensors, (ii) the architecture reduces the variance of the mean-square error of the reconstruction error in comparison with immobile sensors, and (iii) the architecture also allows for rapid generalization (parameterization of dynamics) for data outside the training set. Moreover, the path of the sensor can be chosen arbitrarily, provided training data for the spatial trajectory of the sensor is available. The exceptional performance of the network architecture is demonstrated on three applications: turbulent flows, global sea-surface temperature data, and human movement biomechanics.