Towards algorithmic frameworks for nonlinear reduced order modeling in industrial digital twin applications

The digitization of the manufacturing industry has led to the growing adoption of digital twins. Digital twins consist of two main components: high-fidelity simulations and data assimilation throughout the structure's lifecycle [1]. This work focuses on simulation, specifically using reduced-order modeling (ROM) methods to achieve fast, high-fidelity 3D simulations. To enable widespread and dependable use of ROM methods, it is essential to integrate them into industrial software environments. Siemens has recently addressed these challenges by embedding ROM techniques directly into its Simcenter Samcef nonlinear solver. The LATINPGD algorithm was integrated into the source code with minimal interference, using a weakly intrusive reformulation [2]. While initially focused on nonlinear mechanical simulations, the implementation has been extended in this work to transient nonlinear thermal simulations. This integration provides an efficient, user-friendly approach to handling nonlinear mechanical and thermal problems in an industrial setting. The key innovation of this work lies in optimizing the LATIN-PGD method for industrial software integration. The development of an automatic time grid selection strategy improves efficiency by adjusting the temporal resolution based on problem complexity and convergence state, thus accelerating the local stage of the method. Additionally, this work explores the coupling of the LATIN-PGD solver with Simcenter HEEDS, a design space exploration and optimization software. This coupling enhances the capability of the method to handle complex parametric studies, supporting efficient design optimization and rapid simulations within the digital twin framework. [1] Chinesta F, Cueto E, Abisset-Chavanne E et al. FE. Virtual, digital and hybrid twins: a new paradigm in data-based engineering and engineered data. Archives of computational methods in engineering 27 (2020): 105-134. [2] Scanff R., Néron D., Ladevèze P et al. Weakly-invasive LATIN-PGD for solving time-dependent non-linear parametrized problems in solid mechanics. Computer Methods in Applied Mechanics and Engineering, 396 (2022), Article 114999.