Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain.
arXiv:2606. 03936v1 Announce Type: new Abstract: Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters.
By Niccol\`o Perrone, Fanny Lehmann, Stefania Fresca, Filippo Gatti
arXiv:2611.01680v2 Announce Type: replace-cross
Abstract: Reconstructing three-dimensional (3D) complex ocean acoustic fields from sparse measurements is challenging due to highly oscillatory wave st...
By Yifan Sun, Panqi Chen, Weifeng Shi, Xiao Fu, Lei Cheng
The paper introduces tunable latent priors for diffusion models, normalizing flows, and variational autoencoders using nested dropout. These priors allow the latent dimensionality to adapt to each inverse problem, reducing reconstruction errors compared to fixed-complexity models across tasks such as compressed sensing, inpainting, denoising, and phase retrieval. In linear denoising, the authors derive the optimal latent complexity in closed form, linking it to noise level and signal spectrum.
By Sean Gunn, Jorio Cocola, Oliver De Candido, Vaggos Chatziafratis, Paul Hand
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: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
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:2606. 14139v1 Announce Type: new Abstract: Full waveform inversion (FWI) recovers subsurface velocity from seismic recordings by solving a severely ill-posed, nonconvex PDE-constrained optimization.
By Chen Min, Zheng Ma
arXiv:2602. 23214v2 Announce Type: replace-cross Abstract: Plug-and-Play diffusion prior (PnPDP) frameworks have emerged as a powerful paradigm for solving imaging inverse problems by treating pretrained generative models as modular priors.
By Chenhe Du, Xuanyu Tian, Qing Wu, Muyu Liu, Jingyi Yu, Hongjiang Wei, Yuyao Zhang
arXiv:2607. 14193v1 Announce Type: cross Abstract: The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $\kappa^2$ complex.
By Boyuan Deng, Kshitiz Upadhyay, Michael Shields
arXiv:2610.19187v1 Announce Type: cross
Abstract: Full waveform inversion (FWI) is a powerful tool for high-resolution subsurface model reconstruction, but it remains highly nonlinear and ill-posed,...
By Chao Li, Mrinal K. Sen, Sergey Fomel, Yangkang Chen
The paper introduces a Posterior‑Dynamics Framework that leverages pretrained diffusion models as multiscale priors for linear imaging inverse problems such as deblurring, super‑resolution, and inpainting. By constructing a surrogate likelihood centered on the clean image and incorporating diffusion uncertainty, the authors derive continuous posterior dynamics and a tunable Langevin component for adaptive exploration. They prove theoretical guarantees (endpoint consistency, finite‑horizon tracking, weak accuracy) and present the PD‑IMEX sampler, which achieves high‑quality reconstructions with only 100 score evaluations and controllable fidelity‑diversity trade‑offs.
By Zhaoqiang Liu, Tongyao Pang, Ruibing Wang, Yang Zheng