# PhySense: Sensor Placement Optimization for Accurate Physics Sensing

arXiv: https://arxiv.org/abs/2505.18190 · HTML: https://mlsanity.com/paper/2505.18190/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [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)
- [Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers](https://mlsanity.com/paper/2405.17527/) (2024)
- [Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning](https://mlsanity.com/paper/2008.10740/) (2020)
- [RoPINN: Region Optimized Physics-Informed Neural Networks](https://mlsanity.com/paper/2405.14369/) (2024)
- [PySensors: A Python Package for Sparse Sensor Placement](https://mlsanity.com/paper/2102.13476/) (2021)

## Built on by (most cited first, 11 of 11)

- [AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discovery](https://mlsanity.com/paper/2604.05550/) (2026)
- [Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries](https://mlsanity.com/paper/2602.04940/) (2026)
- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [LASER: Learning Active Sensing for Continuum Field Reconstruction](https://mlsanity.com/paper/2604.19355/) (2026)
- [FLUIDSPLAT: Reconstructing Physical Fields from Sparse Sensors via Gaussian Primitives](https://mlsanity.com/paper/2605.18866/) (2026)
- [Brep2Shape: Boundary and Shape Representation Alignment via Self-Supervised Transformers](https://mlsanity.com/paper/2602.07429/) (2026)
- [PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics](https://mlsanity.com/paper/2605.03548/) (2026)
- [Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributions](https://mlsanity.com/paper/2605.06861/) (2026)
- [MTL-FNO: A Lightweight Multi-Task Fourier Neural Operator for Sparse Field Reconstruction](https://mlsanity.com/paper/2605.26718/) (2026)
- [MoNo: Multiscale Optimal Transport Neural Operator for Solving PDEs on General Geometries](https://mlsanity.com/paper/2608.09764/) (2026)
- [PhysFieldBench: Can Multimodal Models Understand Physical Fields?](https://mlsanity.com/paper/2609.34072/) (2026)

## Abstract (arXiv)

Physics sensing plays a central role in many scientific and engineering domains, which inherently involves two coupled tasks: reconstructing dense physical fields from sparse observations and optimizing scattered sensor placements to observe maximum information. While deep learning has made rapid advances in sparse-data reconstruction, existing methods generally omit optimization of sensor placements, leaving the mutual enhancement between reconstruction and placement on the shelf. To change this suboptimal practice, we propose PhySense, a synergistic two-stage framework that learns to jointly reconstruct physical fields and to optimize sensor placements, both aiming for accurate physics sensing. The first stage involves a flow-based generative model enhanced by cross-attention to adaptively fuse sparse observations. Leveraging the reconstruction feedback, the second stage performs sensor placement via projected gradient descent to satisfy spatial constraints. We further prove that the learning objectives of the two stages are consistent with classical variance-minimization principles, providing theoretical guarantees. Extensive experiments across three challenging benchmarks, especially a 3D geometry dataset, indicate PhySense achieves state-of-the-art physics sensing accuracy and discovers informative sensor placements previously unconsidered. Code is available at this repository: https://github.com/thuml/PhySense.