The paper presents a data‑efficient pre‑training framework for neural surrogate models solving PDEs on unstructured 3D geometries. It introduces a geometry‑driven strategy for steady‑state problems that uses intrinsic shape descriptors, and a physics‑driven approach for transient problems that generates synthetic PDE data online. Experiments show faster convergence, higher data efficiency, and improved accuracy during fine‑tuning, especially in low‑data settings.
By Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu, Benjamin Holzschuh, Jan Hagnberger, Mathias Niepert, Nils Thuerey
arXiv:2609.38623v1 Announce Type: new
Abstract: Learning partial differential equation (PDE) dynamics across varying domains is central to predictive modelling and data-driven discovery of governing...
By Yinghao Cheng, Gengxiang Chen, Xu Liu, Qinglu Meng, Yixin Jing, Xiangguo Tang, Wenping Mou, Lihui Wang, Yingguang Li
arXiv:2605. 00760v2 Announce Type: replace Abstract: This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network, the DeepONet framework.
By Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban
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:2609.38916v1 Announce Type: new
Abstract: Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and...
By Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith, Soledad Villar
arXiv:2609.36216v1 Announce Type: new
Abstract: Neural operators are typically trained in a supervised fashion, which requires a dataset to be generated with a classical solver. Training them physics...
By Shizheng Wen, Siddhartha Mishra, Marius Zeinhofer
Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and dimensions. Inspired by the GNN transferability l...
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: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
arXiv:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.
By Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai
arXiv:2607. 07718v1 Announce Type: cross Abstract: Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations.
By Oded Ovadia, Eli Turkel