Neural surrogates for forecasting physical fields from sparse, noisy sensors typically use a spatial window and a temporal history of past snapshots. This study compares the trade‑off between window size and history length against the Bayes‑optimal error, showing that for fields with local dynamics the optimal forecast relies mainly on distant sensors via spatial correlation. Experiments on Burgers flow and the chaotic Kuramoto‑Sivashinsky equation reveal that the benefit of additional snapshots depends on lead time and system stability, leading to design rules that size the window in correlation lengths and split input budgets between window and history based on forecast horizon.
By Ruige Kong
The paper introduces Structured Latent Dynamics (SLD), a method that reconstructs high‑resolution partial differential equation (PDE) trajectories from coarse, downsampled observations. SLD interpolates input in time, applies a learned temporal correction, and updates a hidden state using learned gated responses combined with spatial differences and a Laplacian term. Two Haar wavelet synthesis branches then map the hidden state and refined coarse input to produce fine‑scale fields, achieving lower error than baseline models on several benchmark PDE systems.
By Chenhao Si, Zishan Qian, Shing-Tung Yau, Rongling Wu, Ming Yan
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
By Zixuan Shen (Central South University), Bingchuan Wang (Central South University), Zhi Wang (Nanjing University), Yong Wang (Central South University)
Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution. We introduce RECAST (Recurrent Error Correction And Super-resolution of coarse-grid Trajectories), a machine-learning framework designed to restore this lost accuracy while retaining coarse-grid evolution.
arXiv:2608. 11572v1 Announce Type: new Abstract: Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution.
By Maryam Reza, Farbod Faraji
The study introduces RegimeShift‑Surrogates, a streaming benchmark that tests surrogate models across eight tasks and multiple regimes. It compares revalidation—choosing the model with lowest current‑window validation loss—to stateful adaptive controllers and finds that revalidation consistently outperforms stateful methods, achieving lower mean log regret in most task‑scenario combinations. The results suggest that fresh validation evidence is more valuable than carrying over past evidence when dealing with distribution shifts.
By Harshil Lodhiya
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
By Pierre Cesar (DATAMOVE), Sofya Dymchenko (DATAMOVE), Abhishek Purandare (DATAMOVE), Bruno Raffin (DATAMOVE)
Laminar-turbulent transition governs skin friction, heat transfer and losses in turbomachinery, yet Reynolds-averaged Navier-Stokes (RANS) transition models rely on empirical correlations and hand-cal...
arXiv:2608. 28564v1 Announce Type: cross Abstract: We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels.
By Lorenzo Rizzi, Arie Wortsman Zurich, Bruno Loureiro
arXiv:2509.06154v3 Announce Type: replace
Abstract: Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings bet...
By Dibyajyoti Nayak, Somdatta Goswami
arXiv:2606. 18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate.
By Pierre Marion
arXiv:2607. 23667v1 Announce Type: cross Abstract: A flow surrogate validated on a simple regime is often taken as evidence that the approach will carry to a richer one.
By Georg Winkler, Martin Stoll