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Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision

arXiv:2603.04431v1 Announce Type: new Abstract: Physical fields are typically observed only at sparse, time-varying sensor locations, making forecasting and reconstruction ill-posed and uncertainty-critical. We present SOLID, a mask-conditioned diffusion framework that learns spatiotemporal dynamics from sparse observations alone: training and evaluation use only observed target locations, requiring no dense fields and no pre-imputation. Unlike prior work that trains on dense reanalysis or simulations and only tests under sparsity, SOLID is trained end-to-end with sparse supervision only. SOLID conditions each denoising step on the measured values and their locations, and introduces a dual-masking objective that (i) emphasizes learning in unobserved void regions while (ii) upweights overlap pixels where inputs and targets provide the most reliable anchors. This strict sparse-conditioning pathway enables posterior sampling of full fields consistent with the measurements, achieving up t

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Kevin Valencia, Xihaier Luo, Shinjae Yoo, David Keetae Park · · 1 min read · 2 views
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arXiv:2603.04431v1 Announce Type: new Abstract: Physical fields are typically observed only at sparse, time-varying sensor locations, making forecasting and reconstruction ill-posed and uncertainty-critical. We present SOLID, a mask-conditioned diffusion framework that learns spatiotemporal dynamics from sparse observations alone: training and evaluation use only observed target locations, requiring no dense fields and no pre-imputation. Unlike prior work that trains on dense reanalysis or simulations and only tests under sparsity, SOLID is trained end-to-end with sparse supervision only. SOLID conditions each denoising step on the measured values and their locations, and introduces a dual-masking objective that (i) emphasizes learning in unobserved void regions while (ii) upweights overlap pixels where inputs and targets provide the most reliable anchors. This strict sparse-conditioning pathway enables posterior sampling of full fields consistent with the measurements, achieving up to an order-of-magnitude improvement in probabilistic error and yielding calibrated uncertainty maps (\r{ho} > 0.7) under severe sparsity.

Executive Summary

This article introduces SOLID, a novel mask-conditioned diffusion framework that learns spatiotemporal dynamics from sparse observations alone. By training on sparse supervision only and conditioning each denoising step on measured values and locations, SOLID achieves an order-of-magnitude improvement in probabilistic error and yields calibrated uncertainty maps. The framework's strict sparse-conditioning pathway enables posterior sampling of full fields consistent with measurements, addressing a long-standing challenge in field reconstruction. The authors' approach has significant implications for various applications, including weather forecasting, oceanography, and climate modeling.

Key Points

  • ▸ SOLID is a mask-conditioned diffusion framework that learns spatiotemporal dynamics from sparse observations alone.
  • ▸ The framework uses sparse supervision only and conditions each denoising step on measured values and locations.
  • ▸ SOLID achieves an order-of-magnitude improvement in probabilistic error and yields calibrated uncertainty maps.

Merits

Strength in Addressing Uncertainty

SOLID effectively addresses the long-standing challenge of uncertainty in field reconstruction, providing calibrated uncertainty maps and improving probabilistic error by an order of magnitude.

Flexibility and Applicability

The framework's ability to learn from sparse observations alone makes it highly flexible and applicable to various fields, including weather forecasting, oceanography, and climate modeling.

Demerits

Limited Experimental Validation

While the authors demonstrate impressive results on a specific dataset, further experimental validation on diverse datasets and real-world applications is necessary to fully assess the framework's generalizability.

Potential Computational Complexity

The diffusion-based architecture and mask-conditioning approach may introduce computational complexity, which may be a challenge for large-scale applications or real-time processing.

Expert Commentary

This article presents a groundbreaking approach to field reconstruction, addressing the long-standing challenge of uncertainty in a novel and effective manner. While some limitations and computational complexity concerns are raised, the framework's potential for improving the accuracy and reliability of field reconstruction and prediction makes it a significant contribution to the field. As with any pioneering work, further experimental validation and exploration of the framework's applicability are essential to its widespread adoption and impact.

Recommendations

  • ✓ Future research should focus on experimental validation of SOLID on diverse datasets and real-world applications to assess its generalizability and scalability.
  • ✓ Investigating the framework's extension to other domains, such as image and signal processing, could unlock further applications and insights.

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