两篇新的研究论文介绍了一种新颖的神经算子架构，旨在提高求解偏微分方程（PDE）的效率和准确性。第一种，线非线性融合神经算子（LNF-NO），将线性和非线性效应解耦，以实现更快的训练和更好的可解释性。第二种，Shearlet 神经算子（SNO），用 Shearlet 替换傅里叶变换，以更好地处理激波主导和多尺度问题中常见的各向异性结构和尖锐梯度。 AI
影响 引入了新的神经算子架构，有望加速科学模拟并提高复杂物理系统的准确性。
排序理由 两篇在 arXiv 上发表的学术论文，介绍了用于求解 PDE 的新颖神经算子架构。
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arXiv:2604.25181v1 Announce Type: new Abstract: Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier repres…
arXiv:2603.24143v2 Announce Type: replace Abstract: Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution …
Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier representations, which can be inefficient for resolvin…