结合深度算子学习的等几何分析求解电磁散射问题
Solving Electromagnetic Scattering Problems by Isogeometric Analysis with Deep Operator Learning
AI总结：
本文提出一种结合等几何分析与深度算子网络的混合方法求解电磁散射问题，通过输入CAD表示预测满足de Rham协调B样条基的电磁场，并在损失函数中引入物理约束，实验证明该方法能以最优速率准确预测电场并具备对未见几何形状的泛化能力。
摘要：
我们提出了一种将等几何分析与深度算子网络相结合的混合方法来求解电磁散射问题。该神经网络以计算机辅助设计表示作为输入，并在de Rham协调的B样条基中预测电磁场，从而例如保证了电场切向连续性的满足。在训练过程中，物理问题被包含在损失函数中。我们的数值结果表明，训练好的网络能准确预测电场，并以最优速率收敛于解析解。此外，在多种几何形状上的训练突显了该网络的泛化能力，在应用于训练集中未包含的新几何形状时，仅产生微小的误差增加。
英文摘要：
We present a hybrid approach combining isogeometric analysis with deep operator networks to solve electromagnetic scattering problems. The neural network takes a computer-aided design representation as input and predicts the electromagnetic field in a de Rham conforming B-spline basis such that for example the tangential continuity of the electric field is respected. The physical problem is included in the loss function during training. Our numerical results demonstrate that a trained network accurately predicts the electric field, showing convergence to the analytical solution with optimal rate. Additionally, training on a variety of geometries highlights the network's generalization capabilities, achieving small error increases when applied to new geometries not included in the training set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
