论文标题
可变输入深度操作员网络
Variable-Input Deep Operator Networks
论文作者
论文摘要
现有用于操作员学习的体系结构要求传感器的数量和位置（评估输入功能的位置）在所有培训和测试样本中保持不变，从而显着限制了其适用性范围。我们通过提出一个新型的操作员学习框架来解决此问题，该框架称为可变输入深度操作员网络（Vidon），该框架允许随机传感器的数字和位置在样本中变化。 Vidon是传感器位置的排列不变的，被证明是近似一类连续运算符的通用。我们还证明，Vidon可以有效地近似PDE中产生的运算符。提出了具有多种PDE的数值实验，以说明Vidon在学习操作员中的稳健性能。
Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their applicability. We address this issue by proposing a novel operator learning framework, termed Variable-Input Deep Operator Network (VIDON), which allows for random sensors whose number and locations can vary across samples. VIDON is invariant to permutations of sensor locations and is proved to be universal in approximating a class of continuous operators. We also prove that VIDON can efficiently approximate operators arising in PDEs. Numerical experiments with a diverse set of PDEs are presented to illustrate the robust performance of VIDON in learning operators.
