# On the application of generative adversarial networks for nonlinear modal analysis

arXiv: https://arxiv.org/abs/2203.01229 · HTML: https://mlsanity.com/paper/2203.01229/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 2 Mar 2022.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Orthogonal Wasserstein GANs](https://mlsanity.com/paper/1911.13060/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [A generative adversarial network optimization method for damage detection and digital twinning by deep AI fault learning: Z24 Bridge structural health monitoring benchmark validation](https://mlsanity.com/paper/2511.00099/) (2025)
- [Structural System Identification via Validation and Adaptation](https://mlsanity.com/paper/2506.20799/) (2025)

## Abstract (arXiv)

Linear modal analysis is a useful and effective tool for the design and analysis of structures. However, a comprehensive basis for nonlinear modal analysis remains to be developed. In the current work, a machine learning scheme is proposed with a view to performing nonlinear modal analysis. The scheme is focussed on defining a one-to-one mapping from a latent `modal' space to the natural coordinate space, whilst also imposing orthogonality of the mode shapes. The mapping is achieved via the use of the recently-developed cycle-consistent generative adversarial network (cycle-GAN) and an assembly of neural networks targeted on maintaining the desired orthogonality. The method is tested on simulated data from structures with cubic nonlinearities and different numbers of degrees of freedom, and also on data from an experimental three-degree-of-freedom set-up with a column-bumper nonlinearity. The results reveal the method's efficiency in separating the `modes'. The method also provides a nonlinear superposition function, which in most cases has very good accuracy.