arXiv:2606. 09923v1 Announce Type: cross Abstract: Neural operators such as the Fourier Neural Operator (FNO) have emerged as powerful surrogates for solving partial differential equations (PDEs), achieving speedups of several orders of magnitude over traditional numerical solvers.
By Michael Chin
arXiv:2606. 01179v1 Announce Type: cross Abstract: Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems.
By Biswajeet Sahoo, Debadutta Patra
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
By Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.
By Handi Zhang, Adrienne M. Propp, Brooks Kinch, Houman Owhadi, Nathaniel Trask
arXiv:2606. 08343v1 Announce Type: new Abstract: We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space.
By Jason Sulskis, Sathya Ravi
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
By Xizhe Wang, Xiaobin Song, Hongbo Zhao, Qingshan Jia, Qianchuan Zhao, Hao Sun, Benben Jiang