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.
By Linzheng Wang, Jason Chen, Nicolas Tricard, Zituo Chen, Xingsen Guo, Sili Deng
arXiv:2610.16645v1 Announce Type: cross
Abstract: Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representatio...
By Ramzi Idoughi, Radouan Boukharfane, Peter Wonka
TRACE is a retrospective streaming generative reconstruction framework designed to recover continuous physical fields from sparse, structured sensing streams. It performs approximate Bayesian inference in a continuous-coordinate latent space, fuses sparse off‑grid measurements with a state‑space temporal prior via Kalman‑style filtering, and refines past frames through retrospective smoothing. Experiments on active matter, ocean sound‑speed fields, and supernova simulations demonstrate that TRACE matches or surpasses existing frame‑wise generative reconstructors, offline spatiotemporal methods, and streaming data‑assimilation baselines in reconstruction quality under temporally sparse and spatially localized sensing protocols.
By Xinyu Zhang, Lihao Chen, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang
arXiv:2507. 03094v2 Announce Type: replace-cross Abstract: Many challenges in scientific imaging involve solving ill-posed inverse problems, where the goal is to recover spatio-temporal fields from indirect, noisy, and highly sparse measurements - often without access to ground truth data or reliable simulators.
By Ali SaraerToosi, Renbo Tu, Esther Y. H. Lin, Kamyar Azizzadenesheli, Aviad Levis
The paper introduces Observation‑Aligned Two‑Stage Domain Decomposition Physics‑Informed Neural Networks (TSDD‑PINN) for reconstructing traffic speed fields from sparse fixed sensors. It first trains a global PINN, then uses its residuals to partition the domain and warm‑start child networks, allowing spatial, temporal, or space‑time refinement. Experiments on the I‑24 MOTION dataset show that TSDD‑PINN achieves lower relative L2 error in most configurations and trains faster than the XPINN baseline, with performance depending on sensing density.
By Eunhan Ka, Ludovic Leclercq, Satish V. Ukkusuri
arXiv:2602.23188v2 Announce Type: replace
Abstract: We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while...
By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi