Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910041465946112 |
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| author | Valencia, Kevin Luo, Xihaier Yoo, Shinjae Park, David Keetae |
| author_facet | Valencia, Kevin Luo, Xihaier Yoo, Shinjae Park, David Keetae |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision Valencia, Kevin Luo, Xihaier Yoo, Shinjae Park, David Keetae Machine Learning Artificial Intelligence 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. |
| title | Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2603.04431 |