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:2610.01759v1 Announce Type: new
Abstract: Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a di...
By Zhenyu Liang, Yining Huang, Yubo Zhao, Jack C. P. Cheng
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
arXiv:2506.12045v2 Announce Type: replace-cross
Abstract: Accurate reconstruction of latent environmental fields from sparse, indirect observations is a fundamental challenge across scientific domain...
By Kazuma Kobayashi, Tapas Tripura, Jay Phil Yoo, Diab Abueidda, Seid Koric, Souvik Chakraborty, Syed Bahauddin Alam
DyPSI is a dynamic physics sensing framework that jointly generates future spatiotemporal fields and sensor trajectories conditioned on past observations. It transforms discrete sensor positions into continuous Sensor Position Fields, encodes both fields and sensing configurations with a shared Functional Tucker representation, and trains a joint diffusion model in a latent space. Experiments on turbulent flow, sea‑surface temperature, and car aerodynamics demonstrate that DyPSI outperforms static and frame‑wise placement strategies, achieving substantial error reductions under tight sensor budgets.
By Yizhou Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Jianfeng Shi, Shikai Fang
arXiv:2506.12045v3 Announce Type: replace
Abstract: Much of the physical world is inaccessible to direct measurement and can be reached only through the sparse traces it leaves in other observable va...
By Kazuma Kobayashi, Tapas Tripura, Jay Phil Yoo, Samrendra Roy, Diab Abueidda, Seid Koric, Souvik Chakraborty, Syed Bahauddin Alam
HarmoCore introduces a generative prior in a compact, continuous latent space for reconstructing oscillatory wave fields from extremely sparse sensor data. It models joint real–imaginary channels using Functional Tucker cores over shared spatial bases, learns a frequency‑conditioned diffusion prior, and performs diffusion posterior sampling directly in core space. Experiments on 2D and 3D Helmholtz problems demonstrate significant performance gains with only 1%–2% sensor coverage while remaining scalable to three dimensions.
By Lihao Chen, Xinyu Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang
arXiv:2609.36527v1 Announce Type: new
Abstract: Recovering complete physical fields from sparse observations is challenging because the measurements may not uniquely determine the underlying state. D...
By Ruichen Xu, Siyao Wang, Fang Wan, Jiacheng Qiu, Wenhan Gao, Jiaxing Zhang, Linsey Pang, Ravid Shwartz-Ziv, Prakhar Mehrotra, Yann LeCun, Yuefan Deng
arXiv:2608. 14744v1 Announce Type: new Abstract: Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation.
By Mrigank Dhingra, Ramchandran Muthukumar, Rebecca Willett, Omer San
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
arXiv:2605.16818v2 Announce Type: replace-cross
Abstract: Learning physical fields directly from incomplete observations is challenging because authentic occlusions are structured, sample-dependent,...
By Chiyuan Ma, Zihan Zhou, Tianshu Yu
arXiv:2607. 20970v1 Announce Type: new Abstract: Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time.
By Weihan Zhang, Xuan Zhao, Yenwen Peng, Yuqi Chen, Jun Tao