The paper discusses how operator‑learning benchmarks are stored as full‑precision arrays that have grown to terabyte scale, and curators must decide how coarsely to compress them. It argues that the usual tolerance on reconstruction error of the stored field is measured in the wrong place, because what matters is the accuracy of a model trained on the compressed copy, not the raw field error. The authors propose a new metric: push a compressed field through a model trained at full precision and compare its output to the output on the clean field, which captures the portion of codec error that actually reaches the model’s output. This metric spans more than two orders of magnitude across six PDE families and correctly orders downstream cost where field error does not, reversing many cross‑dataset comparisons.
By Huy Hoang Le
arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.
By Lennon J. Shikhman
arXiv:2609.24021v1 Announce Type: cross
Abstract: Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying c...
By Daniel Zhengyu Huang, Andrew M. Stuart
arXiv:2610.17221v1 Announce Type: cross
Abstract: Neural surrogates for Partial Differential Equations (PDEs) are usually trained on synthetic data from numerical simulators. As models grow and scali...
By Paul Setinek, Fabian Paischer, Nils Thuerey, Johannes Brandstetter, Felix Koehler
Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying coefficients, initial conditions, forcing terms, bou...
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv:2611.06598v1 Announce Type: new
Abstract: Low-Rank Adaptation (LoRA) adapts a frozen language model through a compact learned update, making it a natural setting for asking how much information...
By Joey David, Paul Caillon, Alexandre Allauzen
arXiv:2606. 15959v1 Announce Type: cross Abstract: Neural networks are used as generative surrogate models for scientific discovery, which are trainable approximations of scientific simulations.
By Zhimin Li, Harshitha Menon, Charles Jekel, Valerio Pascucci, Peter Lindstrom
The paper proposes a training‑free acceleration technique for transformer‑based blind compressed image restoration models. By profiling computation hotspots and channel‑wise activation distributions, the authors identify recurrent projection operators that can be replaced with low‑rank approximations. They introduce Activation‑Calibrated Singular Value Decomposition (ASVD), which derives low‑rank factors offline from pretrained weights and a few calibration images, achieving significant parameter and computation reductions while improving PSNR‑B over a TSVD baseline.
By Suhang Yao, Xin Li, Xijun Wang, Yufei Wang, Yeying Jin, Zhibo Chen
The paper investigates why latent neural surrogate solvers, which compress physical system dynamics into a lower‑dimensional space, often fail during long‑horizon autoregressive rollouts. It demonstrates that training the latent representation only for reconstruction leads to instability, and proposes a set of training interventions—Koopman operator learning, Hamming noise injection, and multi‑step rollout fine‑tuning—that align the latent space with long‑horizon forecasting. These interventions reduce long‑rollout error by about 40 % and achieve accuracy comparable to full‑resolution models while using far fewer floating‑point operations and GPU memory, enabling stable extrapolation in mesoscale crystal‑plasticity simulations of high‑cycle fatigue.
By Andreas E. Robertson, Ashley T. Lenau, John D. Shimanek, Benjamin A. Jasperson, Vivek Oommen, David L. Damm, Krishna Garikipati, Remi Dingreville
arXiv:2606. 27785v1 Announce Type: cross Abstract: Training-free compression methods for large language models (LLMs) often use calibration data to guide compression decisions.
By Qiong Tang, Xiangkun Hu, Xiangyang Liu, Yiran Chen, Yunfan Shao
arXiv:2610.04624v2 Announce Type: replace
Abstract: Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for wh...
By Yida Pan, Muhammad H. Ashiq, Chanyong Jung, Yixuan Jia, Jonah M. Miller, Qing Qu, Ismail Alkhouri