偏微分方程
人工神经网络
操作员(生物学)
领域(数学分析)
参数化复杂度
边值问题
边界(拓扑)
参数统计
有界函数
维数(图论)
应用数学
数学
计算机科学
算法
数学分析
人工智能
纯数学
生物化学
化学
统计
抑制因子
转录因子
基因
作者
Zhiwei Fang,Sifan Wang,Paris Perdikaris
摘要
Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from O(Nd) to O(Nd-1), where d is the domain's dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.
科研通智能强力驱动
Strongly Powered by AbleSci AI