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
arXiv:2607. 26414v1 Announce Type: cross Abstract: Latent low-dimensional structure in datasets of natural and engineered systems enables their sparse sensing, or full-state reconstruction from historical data and very few carefully chosen localized measurements.
By Andrei A. Klishin, J. Nathan Kutz, Krithika Manohar
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:2605. 14285v2 Announce Type: replace-cross Abstract: Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science.
By Yixuan Jia, Siyi Chen, Yida Pan, Xiao Li, Lianghe Shi, Chanyong Jung, Haijie Yuan, Ismail Alkhouri, Yue Cynthia Wu, Saiprasad Ravishankar, Jeffrey A Fessler, Qing Qu
arXiv:2606. 24989v1 Announce Type: new Abstract: Urban flow and air-quality simulations generate high-dimensional datasets describing velocity and pollutant transport across multiple spatial, temporal, and physical-variable dimensions.
By Arindam Sengupta, Paul Jeanney, Ricardo Vinuesa, Jose Miguel Perez, Soledad Le Clainche
arXiv:2606. 17070v1 Announce Type: cross Abstract: Accurate oceanic forecasting is critical for climate monitoring and disaster early warning.
By Qinghui Chen, Zekai Zhang, Hailong Liu, Jinglin Zhang, Cong Bai
This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive.
arXiv:2606. 19562v1 Announce Type: new Abstract: This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations.
By Gabriel F. Barros, R\^omulo M. Silva, Alvaro L. G. A. Coutinho
arXiv:2606. 30699v1 Announce Type: new Abstract: Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning.
By Hao Xu, Siyu Lou, Yuntian Chen, Dongxiao Zhang
arXiv:2604. 23874v3 Announce Type: replace-cross Abstract: The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data.
By Ashwin Suriyanarayanan, Dibyajyoti Chakraborty, Romit Maulik
arXiv:2607. 12975v1 Announce Type: cross Abstract: Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations.
By Zhuoyuan Li, Yue Zhao, Ming Li
arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.
By Ofek Aloni, Barak Fishbain