This work presents a structure-preserving data-driven framework for the modeling and time integration of complex dynamical systems with and without memory effects. The proposed methodology combines nonlinear dimensionality reduction, thermodynamically consistent latent dynamics, and sequence-based neural integrators in order to accurately predict long-time system evolution while respecting fundamental physical principles [1]. An encoder–decoder architecture is first employed to construct a low-dimensional latent representation of the physical state, ensuring accurate reconstruction with controlled compression. On this latent space, two complementary integration strategies are investigated. In the first one, the temporal evolution is governed by a learned metriplectic formulation consistent with the GENERIC framework, enforcing the degeneracy and symmetry properties associated with reversible and irreversible dynamics. In the second approach, a Transformer-based model is used to integrate the latent dynamics by exploiting temporal context windows and attention mechanisms [2]. The proposed framework is assessed on three representative benchmark problems of increasing complexity: incompressible flow past a cylinder, viscoelastic Couette flow modeled with the Oldroyd-B constitutive equation, and Couette flow with a FENE-type polymer model, the latter two exhibiting pronounced memory effects. Numerical results demonstrate that the metriplectic neural network accurately captures short- and medium-term dynamics while preserving thermodynamic structure, whereas the Transformer-based integrator achieves superior long-term predictive accuracy in memory-dominated regimes. The comparison highlights the respective strengths of structure-preserving and data-driven sequence models for reduced- order modeling of complex fluids. Overall, the proposed approach provides a flexible and physically grounded framework for the data-driven simulation of dynamical systems arising in computational mechanics and fluid dynamics. REFERENCES [1] Tierz, A., et al. (2025). On the Feasibility of Foundational Models for the Simulation of Physical Phenomena. International Journal for Numerical Methods in Engineering, 126(6), e70027. [2] Geneva, N., & Zabaras, N. (2022). Transformers for modeling physical systems. Neural Networks, 146, 272–289.