PhySense: Sensor Placement Optimization for Accurate Physics Sensing

TL;DR

PhySense tackles the dual challenge of reconstructing dense physical fields from sparse observations and optimally placing sensors to maximize information. It introduces a flow-based reconstructor trained with cross-attention to handle arbitrary sensor placements, coupled with a projected gradient descent scheme to enforce spatial constraints during sensor-placement optimization. Theoretical analysis links the flow-loss objective to classical A-optimality, providing variance-based guarantees for near-optimal sensor configurations. Empirically, PhySense achieves state-of-the-art reconstruction accuracy across turbulent flow, global sea temperature, and 3D car aerodynamics benchmarks, notably discovering informative placements that outperform traditional methods.

Abstract

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.

Figures (10)

• Figure 1: Performance comparison under same reconstruction model but different sensor placements. (a) Random placement yields poor results due to inadequate spatial coverage. (b) Our optimized placement achieves accurate reconstruction by discovering informative regions, including side mirrors.
• Figure 2: (a) PhySense works as a closed-loop physics sensing paradigm that iteratively co-optimizes sensor placements and reconstruction quality under the reconstruction feedback. (b) Reconstruction stage: A flow-based model with cross-attention mechanisms trained to process arbitrary sensor placements ('$\dashleftarrow$' indicates information flow for subsequent generation and placement optimization).
• Figure 3: Placement optimization stage: Based on a well-trained reconstructor, sensors are optimized by geometry‑constrained projected gradient descent to minimize the flow loss with theoretical guarantees.
• Figure 4: (a) Reconstruction loss versus the number of sensors. Random sampling, classical SSPOR, and our optimized method are compared using the same PhySense reconstruction base model. (b) Visualization of reconstruction results, error maps, and sensor placements (denoted by $\star$). Our optimized placement clearly outperforms the other two strategies on turbulent flow benchmark.
• Figure 5: Different placement strategies comparison and case study on the sea temperature benchmark.

Theorems & Definitions (8)

• Theorem 3.1: Flow-based reconstructor is an unbiased estimator of physical fields
• Definition 3.3: Classical A-optimal placement
• Definition 3.4: Flow-loss-minimized sensor placement
• Theorem 3.5: The objectives of two optimal placements are mutually controlled
• proof
• Remark 3.6
• proof
• Remark A.1