SpectONet: A Physics-Guided Spectral Deep Operator Network for Euler-Bernoulli Beam Dynamics

How can neural operator frameworks be improved to better model structural vibration problems, such as those governed by the Euler-Bernoulli beam (EBB) equation, without relying on large, expensive datasets?

The authors introduce SpectONet, a physics-guided deep operator network. Unlike standard DeepONet architectures that typically use uniform sensor placement to sample input functions, SpectONet employs Chebyshev-Gauss-Lobatto (CGL) points. These points are clustered near domain boundaries, which allows the model to better resolve boundary-sensitive structural responses. The framework is trained entirely through physics-informed constraints—incorporating the governing PDE, initial conditions, and boundary conditions into the loss function—thereby eliminating the need for supervised, paired input-output training data.

SpectONet consistently outperformed several strong baselines, including Vanilla DeepONet, PI-DeepONet, PINNs, and CNN-UNet, across both synthetic EBB vibration problems and a real-world bridge vibration dataset. The authors report that SpectONet achieved at least a 64% improvement in prediction error for synthetic cases and at least a 37% improvement for real-world scenarios compared to the baseline models. These results suggest that the combination of spectral sensor placement and physics-informed training provides a more accurate and computationally efficient surrogate model for structural dynamics.

Structural health monitoring and engineering design often require rapid, repeated evaluations of dynamical systems under varying conditions. By enabling accurate predictions without the need for massive labeled datasets and by improving the resolution of boundary-sensitive physics, SpectONet offers a robust tool for real-time structural analysis and decision-making in engineering applications.