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arXiv Machine Learning By Linzheng Wang, Jason Chen, Nicolas Tricard, Zituo Chen, Xingsen Guo, Sili Deng

Sparse Reconstruction by Direct Measurement-to-Field Generation in Function Space

Read the original on arXiv Machine Learning →

Sparse Reconstruction by Direct Measurement-to-Field Generation in Function Space introduces a functional rectified flow framework called Direct Measurement-to-Field Generation (DMF) that learns to generate physical fields directly from sparse measurements. Unlike traditional grid-based methods, DMF jointly learns a sensor–global–sensor representation and a generative transport mechanism, enabling dynamic fusion of local grounding with global context to evaluate fields at arbitrary query coordinates. Benchmarks demonstrate that DMF outperforms baselines in scenarios with unknown boundaries, missing high-resolution training data, and unmeasured quantities, while its stochastic ensemble generation provides reliable uncertainty quantification and improved continuous ranked probability scores.

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