A Spectral Neural Operator Framework for Learning the Dynamic Response of Structural Systems from Data

Predicting the time-domain dynamic response of a structure to an arbitrary excitation traditionally requires numerically integrating its governing equation of motion for every new load history, which is computationally costly when many predictions are needed, for example in real-time monitoring or design optimization. Neural operators address this by learning, once, an approximate mapping between the space of input load functions and the space of output response functions, so that new predictions require only a forward evaluation rather than a new numerical integration. This paper develops a spectral neural operator, in the style of the Fourier Neural Operator, for predicting the relative displacement response of a single-degree-of-freedom structural system to random ground-acceleration input. The operator is trained by a closed-form per-frequency least-squares fit rather than iterative gradient descent, and is evaluated on a physics-exact synthetic benchmark with realistic sensor noise. The learned operator recovers the analytic resonance peak of the structure to within ۰.۲% of its true magnitude and achieves a test-set normalized mean-squared error of ۰.۰۱۱ once enough spectral modes are retained to cover the resonance frequency, compared to ۰.۲۲۴ for a time-domain finite-impulse-response baseline of matched parameter count, and reveals a sharp error transition exactly at the mode index corresponding to the structure's natural frequency. These results quantify, on a fully reproducible benchmark, why representing structural dynamics in the frequency domain is a parameter-efficient inductive bias for operator learning.

کلیدواژه ها:

neural operators ، Fourier neural operator ، deep learning ، structural dynamics ، operator learning ، spectral methods ، surrogate modeling ، structural health monitoring