  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
