A significant limitation of applying neural networks to scientific computing is their reliance on large datasets. This challenge is particularly acute when data are expensive to acquire, such as when they come from experiments. A promising strategy to mitigate this is to use structure-preserving methods. In this framework, neural networks are architecturally constrained to inherit specific mathematical properties of the underlying physical system, such as symplecticity [1, 2], volume preservation [3], or specific dissipative behavior [4, 5]. While the potential of structure-preserving properties to reduce data requirements has been acknowledged in the literature [6], a systematic study of diverse cases is currently lacking. In this presentation, we provide preliminary results of such a study, evaluating the performance regarding data efficiency of the various structure-preserving architectures mentioned above. REFERENCES [1] S. Greydanus, M. Dzamba, and J. Yosinski. Hamiltonian neural networks. Advances in Neural Information Processing Systems, 32, 2019. [2] P. Jin, Z. Zhang, A. Zhu, Y. Tang, and G. E. Karniadakis. SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems. Neural Networks, 132:166–179, 2020. [3] B. Brantner, M. Kraus, Z. Li, and G. de Romemont. Volume-preserving transformers for learning time series data with structure. ESAIM: Proceedings and Surveys, 81:123–144, 2025. [4] S. Xiao, J. Zhang, and Y. Tang. Generalized lagrangian neural networks. arXiv preprint arXiv:2401.03728, 2024. [5] M. D. Hansen, E. Celledoni, and B. K. Tapley. Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics. arXiv preprint arXiv:2505.20370, 2025. [6] Q. Hern´andez, A. Bad´ıas, D. Gonz´alez, F. Chinesta, and E. Cueto. Structure-preserving neural networks. Journal of Computational Physics, 426:109950, 2021.