High-fidelity three-dimensional turbulent flow fields are crucial for scientific and engineering analyses, but direct numerical simulation or high-resolution measurements are costly. The paper introduces a turbulence-aware framework that couples a multiscale neural operator with a state space model and incorporates Navier-Stokes residuals as soft constraints to reconstruct time-resolved 3‑D flow fields from coarse-grained data. The method also uses a mixture-of-experts mechanism for unsupervised adaptation to unknown coarse-graining, and demonstrates reduced reconstruction errors and improved preservation of multiscale spatial structure and coherent temporal evolution on canonical turbulent systems and atmospheric reanalysis data.
The study demonstrates that a wide‑activation deep super‑resolution (WDSR) network can learn to reconstruct unseen two‑dimensional homogeneous isotropic turbulence fields from overlapping patches of a single high‑resolution realization. By training exclusively on these patches, the model achieves extreme super‑resolution factors of x32 and x64, accurately recovering coherent vortical structures and fine‑scale features better than conventional interpolation. Spectral and statistical analyses confirm improved high‑wavenumber energy recovery and multiscale flow characteristics, and comparisons with models trained on multiple full snapshots highlight the advantage of exploiting spatial redundancy within a single realization.
By Arth Sojitra, Muhammad Abid, Omer San
arXiv:2507. 22082v2 Announce Type: replace-cross Abstract: Direct numerical simulation (DNS) accurately resolves all spatio-temporal scales of wall-bounded turbulence but becomes prohibitively expensive as the Reynolds number increases.
By Anuraj Maurya
arXiv:2606. 16765v1 Announce Type: new Abstract: Evaluating neural operators for 3D turbulent flow requires validated datasets with physical benchmarks.
By Lukas Schr\"oder, Shubham Kavane, Harald K\"ostler
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
arXiv:2610.07033v1 Announce Type: new
Abstract: Predicting transient urban winds is fundamental to understanding urban microclimates and designing climate-resilient cities. Building-resolving large-e...
By Yidi Wang, Yunhe Zhang, Jiawei Gu, Ziyue Qiao, Pengyang Wang
The paper introduces flux‑form spatiotemporal neural operators for predicting coarse‑grained dynamics of multiscale PDEs without relying on closure models. It learns a surrogate evolution operator from filtered high‑fidelity data, using Fourier convolution for spatial mixing and a causal kernel with time‑lag attention for temporal mixing. The method incorporates a flux‑form inductive bias to maintain conservation and provides a data‑driven rule for selecting memory length, achieving stable, accurate long‑horizon rollouts on benchmark equations and turbulent flow simulations.
By Junfeng Chen
arXiv:2608. 04222v1 Announce Type: cross Abstract: Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly.
By Yilong Dai, Yiming Sun, Yiheng Chen, Shengyu Chen, Peyman Givi, Xiaowei Jia, Runlong Yu
arXiv:2609. 38977v1 Announce Type: cross Abstract: Neural surrogates have emerged as fast alternatives to the numerical simulation of three-dimensional turbulence.
By Shaoxiang Qin, Yucheng Zhao, Zongyi Li, Liangzhu Leon Wang, Xiongye Xiao
arXiv:2608. 16546v1 Announce Type: cross Abstract: Most super-resolution models learn from paired data by supervising only the final high-resolution output.
By Zikang Zhan
arXiv:2605. 08832v3 Announce Type: replace Abstract: Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields.
By Jonas Weidner, Yeray Martin-Ruisanchez, Daniel Rueckert, Benedikt Wiestler, Julian Suk
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