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PhySense: Sensor Placement Optimization for Accurate Physics Sensing
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Proposes PhySense, a two-stage framework pairing a cross-attention flow-matching reconstructor (DiT/Transolver) with projected gradient descent sensor placement, and proves its flow loss is polynomially bounded against the A-optimal variance objective.
Problem
Physics sensing requires reconstructing dense physical fields from sparse sensors, but existing deep reconstruction methods use random or fixed sensor placements and do not co-optimize placement with reconstruction.
Approach
A flow-matching reconstructor trained over random sensor placements supplies feedback to a projected gradient descent routine that moves sensors within geometric constraints; the flow loss is shown to be a polynomially bounded surrogate of the A-optimal trace objective.
Key results
- On turbulent flow with 30 sensors, PhySense-opt reaches relative L2 0.2157 vs 0.5746 for best baseline Senseiver (62.46% relative reduction).
- On sea temperature, PhySense-opt averages about 40% relative error reduction over the best baseline across sensor counts.
- On car aerodynamics with 15 optimized sensors, relative L2 improves from 0.0465 to 0.0386 (17% over unoptimized PhySense).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| optimize sensor placement rather than use random placement | PhySense on Turbulent Flow · Turbulent Flow (#30 sensors) | relative L2 error: 0.5176 -> 0.2157 | Helped |
| optimize sensor placement rather than use random placement | PhySense on Sea Temperature · Sea Temperature (#15 sensors) | relative L2 error: 0.0520 -> 0.0439 | Helped |
| optimize sensor placement rather than use random placement | PhySense on Car Aerodynamics · Car Aerodynamics (#15 sensors) | relative L2 error: 0.0465 -> 0.0386 | Helped |
| replace cross-attention sparse-input incorporation with an interpolated field (ablation) | PhySense · Turbulent Flow (#30 sensors) | relative L2 error: 0.5176 -> 0.7509 | Hurt |
| replace noise-data mixture feedback with pure noise input (ablation) | PhySense-opt · Turbulent Flow (#30 sensors) | relative L2 error: 0.2157 -> 0.2286 | Hurt |
| replace cross-attention sparse-input incorporation with AdaLN-Zero (ablation) | PhySense · Turbulent Flow (#30 sensors) | relative L2 error: 0.5176 -> >1 | Hurt |
| use PhySense-optimized sensor placements instead of random placements | Senseiver · Turbulent Flow (#30 sensors) | relative L2 error: 0.5746 -> 0.4601 | Helped |
| use grid sampling instead of random placement | PhySense · Turbulent Flow (#30 sensors) | relative L2 error: 0.5176 -> 0.4930 | Helped |
| use Min-Max placement instead of random placement | PhySense · Turbulent Flow (#30 sensors) | relative L2 error: 0.5176 -> 0.5022 | Helped |
| use SSPOR placements instead of random placement | PhySense · Sea Temperature (#15 sensors) | relative L2 error: 0.0520 -> 0.0543 | Hurt |
Surprising findings
- SSPOR's optimized placement performs no better than random sampling on sea temperature, and sometimes worse.
- AdaLN-Zero conditioning for sparse observations yields relative errors near 1, far worse than the proposed cross-attention.
Limitations
- Placement optimization is run with a fixed sensor count and fixed learning rate tuned per benchmark; 15-sensor settings are sensitive to learning rate.
- Theoretical results rely on a conditional Gaussian assumption on the target distribution.
- Car aerodynamics benchmark is small (100 simulated cases) and only compared against two baselines.
Experimental setup
Datasets: Turbulent channel flow (Senseiver setup) GLORYS12 sea surface temperature reanalysis OpenFOAM car aerodynamics simulations on ShapeNet car mesh
Benchmarks: Turbulent flow Sea temperature (GLORYS12) Car aerodynamics
Metrics: relative L2 error
Baselines: SSPOR VoronoiCNN Senseiver S3GM DiffusionPDE
Builds on: flow matching Senseiver DiT Transolver SSPOR
Closest papers by meaning
- Flow Field Reconstruction with Sensor Placement Policy Learning (NeurIPS 2025 · similarity 0.86)
- Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributions (NeurIPS 2026 · similarity 0.84)
- PIED: Physics-Informed Experimental Design for Inverse Problems (ICLR 2025 · similarity 0.83)
- How to Re-enable PDE Loss for Physical Systems Modeling Under Partial Observation (AAAI 2025 · similarity 0.82)
- Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective (NeurIPS 2025 · similarity 0.82)
- Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations (NeurIPS 2025 · similarity 0.82)
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