The paper presents a method for merging fragmented scientific observations into a continuous, differentiable field without sharing raw data or requiring iterative synchronization. By leveraging the additive structure of fixed-basis ridge-regression statistics, each data holder computes local Gram matrices and moment vectors, producing a merged solution mathematically identical to centralized fitting. The authors demonstrate a complete pipeline that reconstructs the field, extracts derivatives, and performs linear regression to infer physical parameters, achieving sub‑percent errors in recovering diffusion coefficients and wave speeds, and validate the approach on 41 years of NOAA sea‑surface temperature data.
By Naveen Mysore
The paper presents a method for merging distributed observations into a continuous, differentiable spline field without sharing raw data or iterative synchronization. By leveraging fixed-basis ridge regression, each data holder computes local Gram matrices and moment vectors, and the merged solution matches centralized fitting exactly. The authors validate the pipeline on four PDEs and real NOAA sea‑surface temperature data, achieving sub‑percent accuracy for linear cases and 5% for the nonlinear Burgers equation, with no degradation from distributed merging.
By Naveen Mysore
The paper introduces Neptune, a method that uses independent coordinate neural networks to infer parameter fields in multi-physics PDEs from sparse measurements. Neptune can accurately estimate parameters with nonlinear, spatiotemporal variations, outperforming existing techniques by reducing estimation errors by up to two orders of magnitude and improving dynamic response predictions by a factor of ten. It also demonstrates strong physical extrapolation, enabling reliable predictions beyond the training data.
By Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti
arXiv:2607. 19147v1 Announce Type: cross Abstract: Data-driven methods have revolutionized ocean modeling, yet current approaches rely heavily on complete reanalysis datasets, imposing computational constraints and limiting model performance to that of the training data.
By Yangyang Kong, Yutong Jiang, Yanhai Gan, Junyu Dong, Feng Gao, Xiaopei Lin
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
Physical-State-Guided Diffusion Sampling (PSG) couples a persistent physical velocity model to a diffusion prior via a Gaussian bridge, allowing the physical state to be refined by waveform fitting while guiding the reverse diffusion process. This approach separates wave‑equation and denoiser gradients, preserving conventional FWI initialization and optimization history. PSG outperforms classical and diffusion‑based baselines on four OpenFWI families, maintains strong structural recovery under noise, and supports large‑scale models like Marmousi, Overthrust, and BP2004 Salt without retraining.
By Chen Min, Haowen Jiang, Zheng Ma, Xiongbin Yan