房屋地震损失的准确估计对减轻地震灾害有着重要意义。现有的机器学习地震损失预测方法大多是分类估计房屋的破坏等级，因此精度受限。对此，利用波动方程作为卷积神经网络的激活函数，依据2011年东日本大地震398 324条建筑物实际震害数据，直接预测损失率，实现损失精细化预测。研究结果表明，波动方程作为激活函数的卷积神经网络模型在均方误差、平均绝对误差和决定系数3个关键评估指标上，均优于传统激活函数，尤其对破坏严重的房屋损失率预测性能拥有显著提升，准确率高达79.47%。此外，波动方程的物理背景赋予模型更强的可解释性，使其不仅能有效预测地震损害，还能够为模型提供理论依据。研究结果可应用于地震损失评估和地震保险的风险定价，同时也为地震工程和机器学习的交叉研究提供了新思路。

Accurate estimation of seismic losses in buildings is crucial for mitigating earthquake disasters. Existing machine learning-based seismic loss prediction methods primarily classify buildings into different damage levels, which limits prediction accuracy. To address this limitation, the wave equation was employed as the activation function in a convolutional neural network (CNN) to directly predict loss rates based on 398 324 actual building damage records from the 2011 Great East Japan Earthquake, thereby enabling refined loss estimation. The results indicate that the CNN model incorporating the wave equation as an activation function outperforms traditional activation functions in three key evaluation metrics: mean squared error, mean absolute error, and the coefficient of determination. Notably, the model demonstrates a significant improvement in predicting loss rates for severely damaged buildings, achieving an accuracy of up to 79.47%. Furthermore, the physical foundation of the wave equation enhances the interpretability of the model, enabling not only effective seismic loss prediction but also providing a theoretical basis for the model itself. The result can be applied to seismic loss assessment and risk pricing in earthquake insurance while also offering new insights into the intersection of earthquake engineering and machine learning.