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English(EN) Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds

FK-PINNs改进了复杂偏微分方程的神经网络训练

作者 PulseAugur 编辑部 · [2 个来源] ·

研究人员开发了一种新方法，以改进物理信息神经网络（PINNs）在求解复杂偏微分方程（PDEs）方面的训练。该技术被称为“FK-PINNs”，在标准的PINN损失函数中引入了一个数据保真项，充当算子级别的预处理器。该方法被证明可以显著降低损失景观的条件数，从而在标准PINNs失效的情况下实现收敛。该方法利用Feynman-Kac泛函的蒙特卡洛平均来生成标签，并为具有tanh激活的网络提供非渐近误差界。 AI

影响 引入了一种新颖的技术，以增强用于科学模拟的神经网络的稳定性和性能。

排序理由 该集群包含一篇详细介绍新研究方法的学术论文。

在 arXiv stat.ML 阅读 →

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FK-PINNs改进了复杂偏微分方程的神经网络训练

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报道来源 [2]

  1. arXiv stat.ML TIER_1 English(EN) · Nathanael Tepakbong, Hanyu Hu, Chengyu Liu, Xiang Zhou ·

    使用带噪声的Feynman-Kac监督来驯服PINNs的损失景观：算子预处理和非渐近误差界

    arXiv:2606.00643v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlyi…

  2. arXiv stat.ML TIER_1 English(EN) · Xiang Zhou ·

    使用带噪声的Feynman-Kac监督来驯服PINNs的损失景观：算子预处理和非渐近误差界

    Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augment…

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