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

2026-07-28

AI Summary

This work addresses the challenges of boundary-sensitive responses and data scarcity in Euler–Bernoulli beam vibration modeling by proposing a physics-informed spectral-method-enhanced Deep Operator Network (DeepONet). The approach integrates DeepONet’s operator learning capability with physical constraints derived from the governing equation and initial-boundary conditions, and innovatively employs a Chebyshev–Gauss–Lobatto non-uniform sensor layout to strengthen finite-dimensional representation near boundaries. Experiments on three synthetic beam vibration problems and one real-world bridge dataset demonstrate that the proposed method reduces prediction errors by at least 64% on synthetic cases and 37% on real data compared to baseline models—including Vanilla DeepONet, PI-DeepONet, PINN, and CNN-UNet—significantly improving both accuracy and generalization performance.

Abstract

This paper proposes a novel physics-guided spectral deep operator network, termed SpectONet, for solving Euler-Bernoulli beam (EBB) vibration problems. The proposed framework integrates the operator-learning capability of DeepONet with physics-informed constraints and Chebyshev-Gauss-Lobatto (CGL) sensor placement. Unlike conventional DeepONet frameworks, which commonly employ uniformly distributed sensors, SpectONet uses nonuniform spectral sensor locations with a higher concentration of points near the domain boundaries. This sampling strategy improves the finite-dimensional representation of boundary-sensitive structural responses while requiring only a limited number of branch-network inputs. The governing beam equation, together with the associated initial and boundary conditions, incorporated into the training objective to promote physically consistent and generalizable predictions. Numerical experiments on three synthetic EBB vibration problems and a real-world bridge vibration dataset demonstrate the effectiveness of the proposed framework. Comparisons with strong baselines such as, Vanilla DeepONet, PI-DeepONet, PINN, and CNN-UNet show that SpectONet consistently achieves lower prediction errors across all considered evaluation metrics. In particular, SpectONet achieves at least \(64\%\) improvement over the considered baseline models across the three synthetic problems and at least \(37\%\) for the real-world problems. These results demonstrate that SpectONet provides an accurate, computationally efficient, and physically consistent operator-learning framework for structural vibration analysis.

Problem

• Euler-Bernoulli beam
• vibration dynamics
• boundary-sensitive response
• structural vibration
• operator learning

Innovation

• Spectral Deep Operator Network
• Physics-Informed Learning
• Chebyshev-Gauss-Lobatto Sampling
• Euler-Bernoulli Beam Dynamics
• Boundary-Concentrated Sensor Placement