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English(EN) From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators

傅里叶神经网络算子为耗散方程实现学习保证

作者 PulseAugur 编辑部 · [2 个来源] ·

研究人员已经为傅里叶神经网络算子（FNOs）在应用于耗散演化方程的时间-T解算子时，建立了近似和学习保证。分析表明，如果FNOs能够稳定地进行谱离散化，它们就可以有效地学习这些算子。该研究推导了FNO近似界限和多项式样本复杂度保证，学习速率取决于输入空间的平滑度、物理域的维度、非线性项和耗散的强度等因素。 AI

影响 为FNOs学习复杂物理系统奠定了理论基础，可能指导未来的模型开发。

排序理由 该集群包含一篇详细介绍傅里叶神经网络算子理论进展的研究论文。

在 arXiv stat.ML 阅读 →

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傅里叶神经网络算子为耗散方程实现学习保证

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报道来源 [2]

  1. arXiv stat.ML TIER_1 English(EN) · Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan Waniorek ·

    从谱方法到傅里叶神经网络算子的样本复杂度界限

    arXiv:2607.00320v1 Announce Type: new Abstract: We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time-$T$ solution operators of dissipative evolution equations. The analysis builds on the premise that FNOs can efficiently approxima…

  2. arXiv stat.ML TIER_1 English(EN) · Nathan Waniorek ·

    从谱方法到傅里叶神经网络算子的样本复杂度界限

    We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time-$T$ solution operators of dissipative evolution equations. The analysis builds on the premise that FNOs can efficiently approximate and learn solution operators whenever these o…

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