Addressing the complexities of multiphysics systems necessitates the resolution of coupled partial differential equations (PDEs), which presents significant challenges in mathematical formulation, numerical analysis, algorithm design, and software engineering. Recent advances in machine learning have enabled novel approaches to these challenges. We have developed physics-informed neural network architectures designed to efficiently navigate the intricacies of multiphysics simulations involving electromechanical coupling. This method facilitates highly unified and flexible solution strategies for coupled nonlinear phenomena with which conventional methods has struggled, substantially streamlining the simulation of complex multiphysics systems.

Topology optimization searches for the optimal structure that satisfies the given constraints, but it is limited by the computationally expensive and time-consuming nature of iterative finite element (FE) analysis. This study proposes a deep learning-based image super-resolution method to accelerate structural topology optimization. First, we start the topology optimization at a low resolution to quickly obtain the optimized structure, and then convert it to a higher resolution structure using an image super-resolution model. Next, using the converted structure as the initial configuration, topology optimization is carried out at this higher resolution to obtain the final structure. In this way, the topology optimization process can be reduced significantly.

Finite Element Analysis (FEA) serves as an effective numerical tool for addressing engineering problems. For complicate problems, however, it is essential to devote considerable attention to mesh generation and the choice of element types. For example, it is important to employ higher-order elements to circumvent solution instability in incompressible analysis. In wave analysis, ensuring mesh refinement, particularly around the wave-affected regions, is crucial for the accuracy of solutions. However, the employment of refined meshes can be resource-demanding, and adaptive mesh refinement throughout the analysis process may require substantial effort. To address these difficulties, we are advancing the development of enriched finite elements, tailored for incompressible and wave analysis, as well as other domains where conventional FEM may fall short.