In mechanical structures like airplanes, cars and houses, noise is generated and transmitted through vibrations. To take measures to reduce this noise, vibrations need to be simulated with expensive numerical computations. Surrogate deep learning models present a promising alternative to classical numerical simulations as they can be evaluated magnitudes faster, while trading-off accuracy. To quantify such trade-offs systematically and foster the development of methods, we present a benchmark on the task of predicting the vibration of harmonically excited plates. The benchmark features a total of 12000 plate geometries with varying forms of beadings, material and sizes with associated numerical solutions. To address the benchmark task, we propose a new network architecture, named Frequency-Query Operator, which is trained to map plate geometries to their vibration pattern given a specific excitation frequency. Applying principles from operator learning and implicit models for shape encoding, our approach effectively addresses the prediction of highly variable frequency response functions occurring in dynamic systems. To quantify the prediction quality, we introduce a set of evaluation metrics and evaluate the method on our vibrating-plates benchmark. Our method outperforms DeepONets, Fourier Neural Operators and more traditional neural network architectures. Code, dataset and visualizations: https://eckerlab.org/code/delden2023_plate

翻译：在飞机、汽车和房屋等机械结构中，噪声通过振动产生并传递。为采取措施降低噪声，需要借助昂贵的数值计算来模拟振动。替代深度学习方法为经典数值模拟提供了有前景的替代方案，其计算速度可快数个数量级，但需权衡精度。为系统量化此类权衡并推动方法发展，我们提出了一个用于预测谐波激励板振动的基准测试。该基准包含总计12000种不同形式的筋条、材料和尺寸的板几何形状及其对应的数值解。针对基准任务，我们提出了一种名为频率查询算子（Frequency-Query Operator）的新型网络架构，该架构被训练为在给定特定激励频率下，将板几何形状映射至其振动模式。通过应用算子学习原理和形状编码隐式模型，我们的方法有效解决了动态系统中高度可变频率响应函数的预测问题。为量化预测质量，我们引入了一套评估指标，并在振动板基准上对该方法进行了评估。我们的方法在性能上超越了DeepONets、傅里叶神经算子及更传统的神经网络架构。代码、数据集与可视化结果：https://eckerlab.org/code/delden2023_plate