arXiv:2604. 01802v2 Announce Type: replace Abstract: Real-time inference of inaccessible interior physical fields from sparse boundary observations is a fundamental but unresolved problem in scientific machine learning, with direct relevance to safety-critical monitoring across many engineering applications.
By William Howes, Jason Yoo, Kazuma Kobayashi, Subhankar Sarkar, Farid Ahmed, Souvik Chakraborty, Syed Bahauddin Alam
Transolver‑σ is a neural PDE solver that jointly models spectral and physical subspaces to improve accuracy in both one‑step and autoregressive rollouts. The method uses adaptive physical-state interactions, Slice‑Residual Physics‑Attention, and an axis‑factorized Fourier operator to enable information exchange between representations. Across five standard PDE benchmarks, Transolver‑σ reduces benchmark‑averaged relative error by 33.4% compared to the strongest baseline and shows strong performance on coupled multiphysics systems and real‑world fluid and combustion data.
By Haonan Shangguan, Hang Zhou, Haixu Wu, Yuezhou Ma, Jianmin Wang, Mingsheng Long
arXiv:2606. 00716v1 Announce Type: new Abstract: Inference and control in engineered physical systems pay a heavy physics cost at deployment: state estimators, inverse-problem solvers, model-predictive controllers, schedulers, and observers are often not closed-form and must re-solve a numerical optimization per instance, with the operator re-supplied each time.
By Tong Wu, Andrew Campbell, Anna Scaglione
arXiv:2608.24049v1 Announce Type: new
Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
By Jihao Zhang, Junyi Guo, Jian-Xun Wang
arXiv:2606. 14934v1 Announce Type: cross Abstract: This work introduces the Separable Neural Architecture (SNA), a function representational class combining neural approximation with tensor decomposition.
By Reza T Batley, Andrew Kichline, Sourav Saha
The paper introduces Shallow Recurrent Decoder (SHRED) networks as a data‑driven method for accurate state estimation in engineering systems, specifically applied to the TRIGA Mark II research reactor. SHRED maps sparse sensor measurements to the full state space, handling noisy data and requiring minimal training time. The study demonstrates SHRED’s performance using both synthetic CFD data and experimental temperature recordings, achieving low reconstruction errors and showcasing its potential for real‑time monitoring and digital twin development.
By Stefano Riva, Carolina Introini, Jos\`e Nathan Kutz, Antonio Cammi