Title: PhySense: Sensor Placement Optimization for Accurate Physics Sensing
Venue: NeurIPS 2025
Accepted: yes
Keywords: Physics sensing

sensor placement

flow models
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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents a framework for efficient reconstruction of physical fields. This is done by training a flow-based generative model which can reconstruct the physical field from sparse observations, and a method to select the optimal sensor readings to select based on a differentiable objective function that can be optimised with projected GD.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The proposed problem seems to have real use case and is of interesting scope. The proposed solution is also interesting.\n- The benchmarks used seem to be of sufficient difficulty (although it would also be interesting to see more realistic data used instead of simulated ones). \n- Theoretical results seem to be sufficient for the claims that are made by the paper. The link to OED methods is also a good point.\n\nWeaknesses:\n- The reported results have no error bars or confidence intervals (e.g., across the different reconstructed field cases), making it difficult to evaluate how statistically significant the results are.\n- Since the paper does also seem to focus on the sensor placement aspect, it would be interesting to see how other point selection method would work in this problem (e.g., grid placement or some configuration where the sensors are more spread out, or selection based on other ED optimality criteria), and how those placements may affect the other reconstruction methods proposed. This aspect is quite crucial to provide a more convincing and fair comparison with other methods.\n- The motivations could probably be discussed more explicitly, especially with why a quick reconstructor or even a flow-based model specifically needs to be used in this case (I don't doubt that there isn't one, but that the paper would be more complete if that was discussed).\n\nQUESTIONS:\n1. How efficient to train the generative models in the first place, both in terms of the time required and the number of training samples or simulations that have to be used?\n\n2. How would the other sparse reconstruction methods work if a better sensor placement is used? This could potentially make the use of flow models more convincing.\n\n3. Related, why would a flow based model be required in this case? Other alternatives apart from those discussed in the paper would be things such as some encoder/decoder model (that can also quite directly generate the reconstructed field), traditional numerical solvers or even PINNs or PINOs which are known to work for inverse problems. I suspect one of the reason may be the uncertainty quantification although this is not clearly demonstrated in the presented results. Other reasons should also exist which would make the paper motivation stronger.\n\n4. Are the selected sensor placements interpretable or have some characteristics in any way? Furthermore, how sensitive are they to the GD process -- i.e., if I initialise my optimisation differently would the recovered sensor placements change?\n\nLIMITATIONS:\nSome limitations are discussed.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-19"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper investigates physics‐sensing problems—reconstructing dense physical fields from sparse measurements—by jointly learning (i) a flow-matching generative reconstructor conditioned on arbitrary sensor sets and (ii) a geometry-aware projected-gradient algorithm that relocates sensors to near-A-optimal positions. A key theoretical result shows that minimizing the “flow loss” used in placement optimization yields a two-sided quadratic bound on classical A-optimality  along with a theorem that establishes unbiasedness of the reconstructor. Experiments on three benchmarks—channel turbulence, global sea-surface temperature, and 3-D car aerodynamics—report up to 62 % lower reconstruction error than prior art and reveal non-obvious optimal sensor layouts.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- Coupling flow-matching reconstruction with a placement optimizer that is differentiable and geometry-constrained is novel & elegant.\n- The polynomial control between flow loss and A-optimality provides a formal link missing in some other (but not all!) sensor-placement works\n- Evals are comprehensive: 3 diverse domains (regular grid, land–sea mask, unstructured 3-D mesh) demonstrate both generality and significant gains over five baselines, including strong generative models\n- Ablation and diagnostics are good, attention visualizations build reader confidence in the design choices\n- the optimized 15-sensor sea-temperature setup achieves accuracy comparable to 100 random sensors, hinting at real cost savings in field deployments\n\nWeaknesses\n- While the manuscript demonstrates strong empirical gains, the chain that links the algorithm’s design choices to those gains is still opaque. I am unsure why it outperforms both classical A-optimal design and recent deep surrogates. \n- Theorem 3.5 proves a quadratic relation to A-optimality in expectation, but the paper never shows that low flow-loss actually correlates with low test MSE in practice.\n- The benchmarks are legitimate, but I have seen better results on these benchmarks with other classical methods (Even with QDEIM, which is a lightning fast method with good bounds)\n- Where is the physics in the method? It is being applied to fields... The `physics' itself is not utilized. The model would behave identically if the snapshots came from video frames, as long as the tensors have the same shape.\n\nQUESTIONS:\nHow critical is the Conditional-Gaussian Assumption for optimality? Perhaps take a toy problem and evaluate it?\n\nEvaluate robustness or extend analysis to sub-Gaussian / heavy-tailed priors; provide empirical test with non-Gaussian toy problem?\n\nAverage absolute gradient of the reconstruction error w.r.t. each potential location, overlaid with final sensor positions. This could reveal whether the optimiser gravitates to high-information or high-variance locations.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes PhySense, a two-stage approach that both reconstructs a physical field from sparse sensing data, as well as optimizes the sensor locations to be optimal. The paper first uses a flow-based generative model to generate the physical field conditioning on a sparse set of measurement data. This learns a conditional generative model given input of different numbers and locations of the sensors. Then, the learned generator is used to refine the set of sensors' locations. The paper provides both theoretical and experimental guarantees about the convergence and performance gain compared to existing models.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n1. The paper has a strong theoretical section in which it proves some theoretical guarantees of their method's convergence. These theoretical analysis boosts the credibility of the paper's method and their experimental performance. \n2. Compared to previous works that only focus on reconstructing the physical field, the paper proposes a novel joint optimization of both the physical field and the sensor locations, showing that a joint optimization of both fronts would lead to better performance. \n3. The experimental section contains multiple settings covering a wide range of physical phenomena. The proposed method achieves non-trivial improvements over the existing methods in all these settings, demonstrating the effectiveness of their approach. \n\n## Weaknesses\n1. From reading the paper, it seems that no physical constraints are used when learning the generative model. Would adding some sort of physically informed loss would help with the reconstruction? \n2. I found it hard to motivate the physical meaning of the optimized sensor locations in the second stage of the method. The sensor location optimization seems to be finding the optimal sensor configuration based on the learned generative model, so I wonder if there is some kind of overfitting happening when doing the second stage optimization. For example, would the physical field reconstructed using other methods with the optimized sensor locations improve?\n\nQUESTIONS:\n1. How is the flow loss calculated in Eq.(2)? I thought the optimization is performed during test time and the ground truth physical field (i.e., $X_1$) is not available. \n2. Assumption 3.2: Is this assumption reasonable? Why would it be reasonable to assume that the target physical field follows a zero-mean Gaussian distribution? \n3. The paper only evaluates the L2 loss of the modeled field. Is this a reasonable metric? I would imagine that the reconstructed physical field would be used for downstream applications that involve perhaps other quantities from the field (e.g., gradients, Hessians).\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nPhySense proposes a two-stage reconstruction model that uses an efficient flow based generative model to infer a reconstructed physical field conditioned on a set of sparse pointwise sensor measurements, then updates sensor positions by performing a gradient step that improves reconstruction accuracy and then projects sensor positions back to the domain (e.g. any set the sensors are restricted to). This process is repeated for a fixed number of rounds and –as the paper proves–is guaranteed to produce the A-optimal (e.g. variance minimizing) set of sensor positions. The novel use of flow matching in this setting already leads to improved one-shot reconstructions of physical fields over a range of prior works and the additional optimized sensor placement further improves performance. The framework is general enough that–as the paper demonstrates in experiments–the particular architecture of the velocity field can be interchanged depending on the specific application.\n\nSTRENGTHS AND WEAKNESSES:\nstrengths:\n1. The presentation is exceedingly clear, providing excellent background and intuition on the three core areas leveraged in the method: sparse reconstruction, optimized sensor placement, and flow-based matching. I found the method section very easy to follow as a result, despite the fact that it incorporates many disparate subfields.\n\n2. The method is straightforward, yet relies on an elegant theory proving that A-optimality is obtained through performing gradient descent on the flow residual with respect to the sensor positions. This raises many interesting follow up questions around how to achieve alternative sensor placement objectives–some of which were summarized earlier in the paper–and the interplay these objectives have on reconstruction methods.\n\nweaknesses\n\n1. The comparison against other reconstruction methods is partially unclear to me. It seems like in the process of optimizing sensor position, PhysSense makes additional measurements and this leads to more effective sensor positions being utilized than in the naive case–even if an equal number of measurements are directly applied to reconstruction. This could also be a misunderstanding on my part though, either in how PhySense is utilizing its sample budget or whether the sensor optimization is run as a pre-processing step using only the domain geometry and sampled PDE solutions.\n\nQUESTIONS:\n* Does PhysSense take additional measurements at each step of projected gradient descent as its optimizing sensor positions? It's not clear to me whether the sensor optimization is a performed with real measurements or generate data.\n* Where does this method stand in relation to approaches like Thompson sampling? Specifically, I'm curious if PhySense can be applied to adaptive sampling problems, where \"sensors\" are not so much a physical device that is being positioned but rather a position at which a measurement is collected (e.g. a camera moving around an object)?\n* On line 191 is the conditional random variable supposed to be centered on 0 or X1(p)?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-03"}