arXiv:2606. 07982v1 Announce Type: new Abstract: High-dimensional transient heat diffusion under noisy boundary conditions exposes a fundamental limitation of classical numerical methods: accuracy degrades catastrophically where physical noise is unavoidable.
By Shreesh Bhattarai, Harish Chandra Bhandari
arXiv:2505. 02979v4 Announce Type: replace-cross Abstract: We propose a novel inverse-modelling approach that estimates the parameters of a simple land-surface model (LSM) by assimilating data into a differentiable, physics-based forward model formulated using convolutional operations.
By Ruiyue Huang, Claire E. Heaney, Maarten van Reeuwijk
Physics-Informed Error Field Learning (PIEFL) is a post‑training optimization framework for Physics‑Informed Neural Networks (PINNs). After a primary network reaches satisfactory accuracy, PIEFL introduces an auxiliary error network that learns the discrepancy between the current approximation and the exact solution by deriving error control equations under physical constraints. The learned error correction is then combined with the primary prediction, improving solution accuracy without modifying the primary network architecture and focusing computational resources on correcting existing prediction errors.
By Jiuyun Sun, Yong Zhang
arXiv:2607. 03682v1 Announce Type: cross Abstract: Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized.
By Zihao Guo, Xin Li, Zhihong Xia
arXiv:2606. 28158v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calder\'on inverse problem from limited boundary data.
By Ali AlHadi Kalout, Pablo Tejerina-P\'erez, Konstantin Karchev, Pedro Taranc\'on-\'Alvarez, Leonid Sarieddine, Raul Jimenez, Max Engelstein, Guy David
arXiv:2606. 13695v1 Announce Type: cross Abstract: Mineral prospectivity modelling (MPM) underpins exploration economics, yet most operational pipelines reduce to data-driven classifiers trained on shallow surface proxies.
By Boris Kriuk