# Data-Driven Sparse Sensor Placement for Reconstruction

arXiv: https://arxiv.org/abs/1701.07569 · HTML: https://mlsanity.com/paper/1701.07569/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2017.

## Built on by (most cited first, 30 of 57)

- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data](https://mlsanity.com/paper/2204.03216/) (2022)
- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [The transformative potential of machine learning for experiments in fluid mechanics](https://mlsanity.com/paper/2303.15832/) (2023)
- [A DeepONet multi-fidelity approach for residual learning in reduced order modeling](https://mlsanity.com/paper/2302.12682/) (2023)
- [Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction](https://mlsanity.com/paper/2307.11793/) (2023)
- [PhySense: Sensor Placement Optimization for Accurate Physics Sensing](https://mlsanity.com/paper/2505.18190/) (2025)
- [Guiding diffusion models to reconstruct flow fields from sparse data](https://mlsanity.com/paper/2510.19971/) (2025)
- [PySensors: A Python Package for Sparse Sensor Placement](https://mlsanity.com/paper/2102.13476/) (2021)
- [A Machine Learning Surrogate Modeling Benchmark for Temperature Field Reconstruction of Heat-Source Systems](https://mlsanity.com/paper/2108.08298/) (2021)
- [Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environments](https://mlsanity.com/paper/2506.00214/) (2025)
- [Constrained optimization of sensor placement for nuclear digital twins](https://mlsanity.com/paper/2306.13637/) (2023)
- [Active operator inference for learning low-dimensional dynamical-system models from noisy data](https://mlsanity.com/paper/2107.09256/) (2021)
- [Differentiable Feature Selection, a Reparameterization Approach](https://mlsanity.com/paper/2107.10030/) (2021)
- [Artificial intelligence-driven digital twin of a modern house demonstrated in virtual reality](https://mlsanity.com/paper/2212.07102/) (2022)
- [Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems; a New Approach Using Secants](https://mlsanity.com/paper/2101.11162/) (2021)
- [Data-Induced Interactions of Sparse Sensors Using Statistical Physics](https://mlsanity.com/paper/2307.11838/) (2023)
- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [Model discovery in the sparse sampling regime](https://mlsanity.com/paper/2105.00400/) (2021)
- [Super-resolution GANs of randomly-seeded fields](https://mlsanity.com/paper/2202.11701/) (2022)
- [GN-SINDy: Greedy Sampling Neural Network in Sparse Identification of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/2405.08613/) (2024)
- [Predictive Digital Twin for Condition Monitoring Using Thermal Imaging](https://mlsanity.com/paper/2411.05887/) (2024)
- [Time-Vertex Machine Learning for Optimal Sensor Placement in Temporal Graph Signals: Applications in Structural Health Monitoring](https://mlsanity.com/paper/2512.19309/) (2025)
- [Reconstruction of Fields from Sparse Sensing: Differentiable Sensor Placement Enhances Generalization](https://mlsanity.com/paper/2312.09176/) (2023)
- [Computationally and Memory-Efficient Robust Predictive Analytics Using Big Data](https://mlsanity.com/paper/2403.19721/) (2024)
- [Revisiting Score Function Estimators for k-Subset Sampling](https://mlsanity.com/paper/2407.16058/) (2024)
- [Physics-aligned Schr"odinger bridge](https://mlsanity.com/paper/2409.17825/) (2024)
- [State Estimation Using Sparse DEIM and Recurrent Neural Networks](https://mlsanity.com/paper/2410.15982/) (2024)
- [Attention-Based Reconstruction of Full-Field Tsunami Waves from Sparse Tsunameter Networks](https://mlsanity.com/paper/2411.12948/) (2024)
- [Interpretable Diagnostics and Adaptive Data Assimilation for Neural ODEs via Discrete Empirical Interpolation](https://mlsanity.com/paper/2510.21852/) (2025)

## Abstract (arXiv)

Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent compressibility enables sparse sensing. This article explores optimized sensor placement for signal reconstruction based on a tailored library of features extracted from training data. Sparse point sensors are discovered using the singular value decomposition and QR pivoting, which are two ubiquitous matrix computations that underpin modern linear dimensionality reduction. Sparse sensing in a tailored basis is contrasted with compressed sensing, a universal signal recovery method in which an unknown signal is reconstructed via a sparse representation in a universal basis. Although compressed sensing can recover a wider class of signals, we demonstrate the benefits of exploiting known patterns in data with optimized sensing. In particular, drastic reductions in the required number of sensors and improved reconstruction are observed in examples ranging from facial images to fluid vorticity fields. Principled sensor placement may be critically enabling when sensors are costly and provides faster state estimation for low-latency, high-bandwidth control. MATLAB code is provided for all examples.