English(EN)Do Neural PDE Solvers Learn the Right Dynamics?
新方法提升神经PDE求解器的准确性和效率 · 跟踪4个来源
作者PulseAugur 编辑部·[6 个来源]·
研究人员正在探索训练偏微分方程（PDE）神经求解器的新方法，以提高其准确性和效率。一种方法侧重于在简单预测分数之外评估所学的动力学，提出了一个框架来评估误差形成、集合几何和极端事件。另一种方法为非结构化神经PDE求解器引入了一个数据高效的预训练框架，利用几何驱动和物理驱动策略来减少对昂贵数据集的依赖。此外，一种名为“任意维度机器学习”的技术，利用图神经网络，允许在低维度训练的PDE求解器应用于高维度，并提高性能和降低计算成本。
AI
arXiv:2610.09255v1 Announce Type: new Abstract: Neural PDE surrogates are trained on numerical solver outputs that contain both physical evolution and solver-specific discretization errors. Because surrogates are also evaluated against held-out trajectories from the same solver, …
arXiv cs.LG
TIER_1English(EN)·Chun-Wun Cheng, Bingcheng Hu, Angelica I. Aviles-Rivero·
arXiv:2610.09510v1 Announce Type: new Abstract: Physics-informed neural PDE solvers adapt their parameters to satisfy governing equations, yet their representational structure typically remains fixed throughout training. This rigidity is poorly matched to PDE solutions with stron…
arXiv cs.LG
TIER_1English(EN)·Haonan Li, Yue Song, Bin Yang, Kaihong Luo·
arXiv:2610.06952v1 Announce Type: new Abstract: Neural PDE solvers can achieve low prediction errors, but do they reproduce the dynamics of the systems they model? Prediction scores alone offer an incomplete answer: they measure agreement with reference solutions but provide limi…
arXiv cs.AI
TIER_1English(EN)·Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu, Benjamin Holzschuh, Jan Hagnberger, Mathias Niepert, Nils Thuerey·
arXiv:2610.03363v1 Announce Type: new Abstract: Neural surrogate models for Partial Differential Equations (PDEs) on unstructured 3D geometries are often limited by poor generalization and the high cost of generating large-scale training datasets. Consequently, pre-training on ma…
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 literature, we show mathematical conditions under which a partial differential eq…
arXiv stat.ML
TIER_1English(EN)·Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith, Soledad Villar·
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 dimensions. Inspired by the GNN transferability literature, we show mathematical …
