# A physics-driven sensor placement optimization methodology for temperature field reconstruction

arXiv: https://arxiv.org/abs/2409.18423 · HTML: https://mlsanity.com/paper/2409.18423/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 27 Sep 2024.

## Builds on (most cited first, 19 of 19)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
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- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Data-Driven Sparse Sensor Placement for Reconstruction](https://mlsanity.com/paper/1701.07569/) (2017)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [A novel meta-learning initialization method for physics-informed neural networks](https://mlsanity.com/paper/2107.10991/) (2021)
- [Multi-fidelity sensor selection: Greedy algorithms to place cheap and expensive sensors with cost constraints](https://mlsanity.com/paper/2005.03650/) (2020)
- [PySensors: A Python Package for Sparse Sensor Placement](https://mlsanity.com/paper/2102.13476/) (2021)
- [The Artificial Intelligence behind the winning entry to the 2019 AI Robotic Racing Competition](https://mlsanity.com/paper/2109.14985/) (2021)
- [Temperature Field Inversion of Heat-Source Systems via Physics-Informed Neural Networks](https://mlsanity.com/paper/2201.06880/) (2022)
- [Greedy Sensor Placement with Cost Constraints](https://mlsanity.com/paper/1805.03717/) (2018)
- [Graph Neural Networks for Aerodynamic Flow Reconstruction from Sparse Sensing](https://mlsanity.com/paper/2301.03228/) (2023)
- [Data-driven sparse sensor placement based on A-optimal design of experiment with ADMM](https://mlsanity.com/paper/2010.09329/) (2020)
- [Exploiting Convexification for Bayesian Optimal Sensor Placement by Maximization of Mutual Information](https://mlsanity.com/paper/1906.05953/) (2019)
- [Data-Driven Sensor Selection Method Based on Proximal Optimization for High-Dimensional Data With Correlated Measurement Noise](https://mlsanity.com/paper/2205.06067/) (2022)
- [Fast Greedy Optimization of Sensor Selection in Measurement with Correlated Noise](https://mlsanity.com/paper/1912.01776/) (2019)
- [On the use of recurrent neural networks for predictions of turbulent flows](https://mlsanity.com/paper/2002.01222/) (2020)
- [Randomized Group-Greedy Method for Large-Scale Sensor Selection Problems](https://mlsanity.com/paper/2205.04161/) (2022)

## Abstract (arXiv)

Perceiving the global field from sparse sensors has been a grand challenge in the monitoring, analysis, and design of physical systems. In this context, sensor placement optimization is a crucial issue. Most existing works require large and sufficient data to construct data-based criteria, which are intractable in data-free scenarios without numerical and experimental data. To this end, we propose a novel physics-driven sensor placement optimization (PSPO) method for temperature field reconstruction using a physics-based criterion to optimize sensor locations. In our methodological framework, we firstly derive the theoretical upper and lower bounds of the reconstruction error under noise scenarios by analyzing the optimal solution, proving that error bounds correlate with the condition number determined by sensor locations. Furthermore, the condition number, as the physics-based criterion, is used to optimize sensor locations by the genetic algorithm. Finally, the best sensors are validated by reconstruction models, including non-invasive end-to-end models, non-invasive reduced-order models, and physics-informed models. Experimental results, both on a numerical and an application case, demonstrate that the PSPO method significantly outperforms random and uniform selection methods, improving the reconstruction accuracy by nearly an order of magnitude. Moreover, the PSPO method can achieve comparable reconstruction accuracy to the existing data-driven placement optimization methods.