面向反源问题的谱模型信息神经网络
A Spectral Model-Informed Neural Network for Inverse Source Problems
- Kansas State University（堪萨斯州立大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
提出一种无监督两步模型信息深度学习框架，利用边界数据生成成像函数并推导谱域模型方程，训练神经网络快速准确重建反源问题中的源函数，在二维和三维数值实验中验证了有效性，并在二维情形下优于传统最小二乘法。
中文摘要 AI 辅助
本文提出了一种无监督的两步模型信息深度学习框架，用于求解反源问题。第一步，将边界测量数据转化为一个成像函数，该函数编码了未知源的形状和位置信息。利用这一信息，我们在谱域中推导出一个基于傅里叶的模型方程，该方程将成像函数与源函数的傅里叶系数联系起来。第二步，将该模型方程纳入模型信息神经网络的训练中，以恢复感兴趣的参数。所提出的方法能够快速、准确地重建源函数，同时对噪声保持鲁棒性。通过在二维和三维环境中的数值实验验证了该方法的有效性。对于二维情形，我们进一步将我们的方法与传统的二乘法进行比较，以验证其计算效率和重建精度。
英文摘要
In this paper, we propose an unsupervised, two-step model-informed deep learning framework for solving the inverse source problem. In the first step, boundary measurement data are transformed into an imaging function that encodes information about the shape and location of the unknown source. Leveraging this information, we derive a Fourier-based model equation in the spectral domain that relates the imaging function to the Fourier coefficients of the source function. In the second step, this model equation is incorporated into the training of a model-informed neural network to recover the parameters of interest. The proposed approach enables fast and accurate reconstruction of the source function while maintaining robustness to noise. The effectiveness of the method is demonstrated through numerical experiments in both two- and three-dimensional settings. For the two-dimensional case, we further compare our approach with the traditional least-squares method to validate its computational efficiency and reconstruction accuracy.
