# A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam

arXiv: https://arxiv.org/abs/2601.00866 · HTML: https://mlsanity.com/paper/2601.00866/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 55 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios](https://mlsanity.com/paper/2205.07731/) (2022)
- [Physics-informed neural networks for solving forward and inverse problems in complex beam systems](https://mlsanity.com/paper/2303.01055/) (2023)
- [Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations](https://mlsanity.com/paper/2311.00578/) (2023)
- [Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations](https://mlsanity.com/paper/2407.10836/) (2024)
- [Physics-informed machine learning for moving load problems](https://mlsanity.com/paper/2304.00369/) (2023)
- [MoRPI-PINN: A Physics-Informed Framework for Mobile Robot Pure Inertial Navigation](https://mlsanity.com/paper/2507.18206/) (2025)
- [Physics-Informed Neural Network based Damage Identification for Truss Railroad Bridges](https://mlsanity.com/paper/2502.00194/) (2025)

## Built on by (most cited first, 1 of 1)

- [SpectONet: A Physics-Guided Spectral Deep Operator Network for Euler-Bernoulli Beam Dynamics](https://mlsanity.com/paper/2607.25790/) (2026)

## Abstract (arXiv)

Recent advancements in physics-informed neural networks (PINNs) and their variants have garnered substantial focus from researchers due to their effectiveness in solving both forward and inverse problems governed by differential equations. In this research, a modified Auxiliary physics-informed neural network (A-PINN) framework with balanced adaptive optimizers is proposed for the analysis of structural vibration problems. In order to accurately represent structural systems, it is critical for capturing vibration phenomena and ensuring reliable predictive analysis. So, our investigations are crucial for gaining deeper insight into the robustness of scientific machine learning models for solving vibration problems. Further, to rigorously evaluate the performance of A-PINN, we conducted different numerical simulations to approximate the Euler-Bernoulli beam equations under the various scenarios. The numerical results substantiate the enhanced performance of our model in terms of both numerical stability and predictive accuracy. Our model shows improvement of at least 40% over the baselines.