arXiv:2603. 08465v3 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving fluid-flow PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces (TPMS).
By Weizheng Zhang, Xunjie Xie, Hao Pan, Xiaowei Duan, Bingteng Sun, Qiang Du, Lin Lu
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:2609.14841v1 Announce Type: new
Abstract: Scientific machine learning methods such as physics-informed neural networks (PINNs) increasingly rely on domain decomposition for better scalability w...
By Sidharth S. Menon, Irina Tezaur, Ameya D. Jagtap
The paper introduces a hybrid modeling framework that couples numerics-informed neural networks (NINNs) with classical full order models (FOMs) via the overlapping Schwarz alternating method. It demonstrates that a monolithic NINN can be accurately trained on a two-dimensional advection-diffusion problem in a high Peclet-number regime without domain decomposition, and then uses overlapping multiplicative Schwarz to couple a pre-trained, subdomain-local NINN with a neighboring FOM while keeping the NINN weights fixed during iteration. Two training strategies—top-down, using full-domain FOM-FOM Schwarz data, and bottom-up, generating synthetic boundary traces—both yield hybrid NINN-FOM solutions that closely match the corresponding FOM-FOM Schwarz results.
By George Chumbipuma, Irina Tezaur, Alejandro Diaz, Beatrice Riviere
A new AI-accelerated iterative solver, DAIST, is introduced for 3D-IC thermal modeling. It decomposes a full-package FEM simulation into block-level subdomains, replaces each subdomain solver with a neural operator, and couples them through iterative exchanges of interfacial temperature and heat flux. This approach eliminates the need to retrain models when die count or topology changes and offers a controllable accuracy‑runtime tradeoff, achieving up to 178× speedup with minimal temperature error on tested systems.
By Yixing Li, Jiahang Zhou, Zhiyu Zeng, Xin Ai
The paper presents cross‑domain pretraining for neural surrogates in steady‑state computational fluid dynamics (CFD). By training models across varied geometries, boundary conditions, and fidelities, the authors show that such pretraining improves zero‑ and few‑shot performance compared to training from scratch or transferring from domain‑specific experts. Finetuning a pretrained cross‑domain model can reduce errors by 2–3× at the same sample size and require eight times fewer samples to reach the same error, with benefits that grow with model size and dataset diversity.
By Anthony Zhou, Amir Barati Farimani, Shirley Ho, Rudy Morel