The paper investigates how different attention mechanisms affect the performance of DeepONet neural operators. Five variants—varying in cross‑attention, self‑attention, tokenization, and attention depth—are trained in both data‑driven and physics‑informed settings on one‑ and two‑dimensional PDE benchmarks. Results show that per‑sensor tokenization with cross‑attention consistently reduces error, while branch self‑attention helps only in complex spatial problems, and deeper cross‑attention yields diminishing returns with higher cost.
By Amar Alem Koric, Qibang Liu, Seid Koric
arXiv:2608. 16080v1 Announce Type: new Abstract: Thermal-aware optimization of multi-die 3D integrated circuits evaluates many designs, each a costly heat-equation solve.
By Xinling Yu, Yixing Li, Ziyue Liu, Xin Ai, Zhiyu Zeng, Hai Li, Zheng Zhang
While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the single node bottleneck, where the maximum processable mesh resolution is strictly limited by the VRAM of a single compute unit. To address these challenges, we propose PGD-NO, a neural operator with Precomputed Geometry Decomposition, that relocates the computational overhead of geometric encoding to a deterministic pre-computation phase.
arXiv:2607. 08025v1 Announce Type: new Abstract: While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the single node bottleneck, where the maximum processable mesh resolution is strictly limited by the VRAM of a single compute unit.
By Weiheng Zhong, Jing Bi, Victor Oancea, Hadi Meidani
arXiv:2606. 29440v1 Announce Type: new Abstract: Repeatedly solving parametric PDEs is essential for uncertainty quantification, design optimization and inverse problems, but conventional neural operators require expensive non-convex training.
By Zirui Deng, Jingbo Sun, Deyu Meng, Fei Wang
arXiv:2606. 04582v1 Announce Type: cross Abstract: Real-time monitoring of the temperature distribution within components and sub-structures is a challenging topic in many systems due to restrictions on feasible sensor locations.
By Monika Stipsitz, H\`elios Sanchis-Alepuz, Jacob Reynvaan, Silvester Sabathiel
arXiv:2607. 20321v1 Announce Type: cross Abstract: Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields.
By Tianyu Li, Zhiwei Cao, Qingang Zhang, Ruihang Wang, Binyang Song, Yonggang Wen
The paper introduces equation recast, a method that transforms parametric operator learning into learning a single canonical operator. By analytically deriving parameter-induced variations from the governing equations and incorporating them as effective sources, the approach enables zero‑shot predictions across new parameter regimes and supports extrapolation in multi‑parameter, nonlinear, and singular PDE settings. It also integrates sparse heterogeneous datasets, uses loss of convergence as an internal warning, and demonstrates unification of electron‑temperature data from multiple tokamak geometries in high‑fidelity nuclear fusion simulations.
By Qiyun Cheng, Valentin Duruisseaux, Cesar F. Clauser, Md Hossain Sahadath, Huihua Yang, Shaowu Pan, Nathaniel Ferraro, Anima Anandkumar, Wei Ji, Cristina Rea
arXiv:2602. 11626v3 Announce Type: replace-cross Abstract: Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations.
By Wenqian Chen, Zhi-Feng Wei, Yucheng Fu, Michael Penwarden, Pratanu Roy, Panos Stinis
arXiv:2602. 04940v2 Announce Type: replace Abstract: Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers.
By Hang Zhou, Haixu Wu, Haonan Shangguan, Yuezhou Ma, Huikun Weng, Jianmin Wang, Mingsheng Long
arXiv:2607. 18020v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
By Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai
arXiv:2607. 18020v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
By Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai