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Jun, 2024
Astral: 使用误差主量训练物理知情的神经网络
Astral: training physics-informed neural networks with error majorants
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Vladimir Fanaskov, Tianchi Yu, Alexander Rudikov, Ivan Oseledets
TL;DR
通过引入误差上界作为训练指标,我们提出了一种新的物理信息学习方法,该方法能够可靠地估计近似解与精确解之间的接近程度,并在达到期望精度时停止优化过程,实验证明该方法相对于传统的残差优化方法具有更快的收敛速度和更低的误差。
Abstract
The primal approach to
physics-informed learning
is a
residual minimization
. We argue that residual is, at best, an indirect measure of the error of approximate solution and propose to train with
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