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

arXiv: https://arxiv.org/abs/2607.25790 · HTML: https://mlsanity.com/paper/2607.25790/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 61 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks](https://mlsanity.com/paper/2303.02243/) (2023)
- [Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals](https://mlsanity.com/paper/2302.13368/) (2023)
- [Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving](https://mlsanity.com/paper/2408.02198/) (2024)
- [Diffeomorphism Neural Operator for various domains and parameters of partial differential equations](https://mlsanity.com/paper/2402.12475/) (2024)
- [Predictions of Transient Vector Solution Fields with Sequential Deep Operator Network](https://mlsanity.com/paper/2311.11500/) (2023)
- [Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEs](https://mlsanity.com/paper/2501.08428/) (2025)
- [Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations](https://mlsanity.com/paper/2311.00578/) (2023)
- [Deep neural operator for learning transient response of interpenetrating phase composites subject to dynamic loading](https://mlsanity.com/paper/2303.18055/) (2023)
- [Learning to Predict Structural Vibrations](https://mlsanity.com/paper/2310.05469/) (2023)
- [Exponential stability of damped Euler-Bernoulli beam controlled by boundary springs and dampers](https://mlsanity.com/paper/2307.06170/) (2023)
- [PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations](https://mlsanity.com/paper/2506.01598/) (2025)
- [A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam](https://mlsanity.com/paper/2601.00866/) (2025)

## Abstract (arXiv)

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.