English(EN) Unbiased and Second-Order-Free Training for High-Dimensional PDEs

新方法通过自适应算子变换提升偏微分方程预训练

作者 PulseAugur 编辑部 · [2 个来源] · 2026-05-14 09:59

研究人员开发了AOT-POT，一种在多样化偏微分方程（PDE）数据集上预训练神经算子的新颖方法。该方法将复杂的解算子转换为更简单、对齐的形式，单个神经网络可以有效地对其进行建模。AOT-POT在12个PDE基准测试中取得了最先进的性能，参数增加极少，并显著降低了域内和域外PDE的误差。 AI

影响增强了AI模型解决复杂科学问题的能力，有可能加速依赖偏微分方程的领域的研究。

排序理由发表了一篇关于科学机器学习新方法的学术论文。

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arXiv cs.LG TIER_1 English(EN) · Chao Zhang · 2026-05-15 09:50

AOT-POT：大规模 PDE 预训练的自适应算子变换

Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientific machine learning. However, the inherent complexity and structural diversity of PDE solution opera…
Hugging Face Daily Papers TIER_1 English(EN) · 2026-05-14 09:59

高维偏微分方程的无偏且无二阶自由的训练

Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, …