Non-intrusive mesh-free surrogate models for differential problems in domains of variable shape
Please login to view abstract download link
In this presentation, we present a novel surrogate model, based on artificial neural networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. We employ a mesh-less architecture, thus overcoming the limitations associated with image segmentation and mesh generation required by traditional discretization methods. Our method encodes geometrical variability through scalar landmarks, such as coordinates of points of interest. We present proof-of-concept results obtained with a data-driven loss function based on simulation data. Nonetheless, our framework is non-intrusive and modular, as we can modify the loss by considering additional constraints, thus leveraging available physical knowledge. Our approach also accommodates a universal coordinate system, which supports the surrogate model in learning the correspondence between points belonging to different geometries, boosting prediction accuracy on unobserved geometries. Finally, we present several numerical test cases in computational fluid dynamics and computational mechanics involving computational domains of variable shape and even topology. The results show that our method allows for inexpensive but accurate approximations of the solution, avoiding computationally expensive image segmentation, mesh generation, or re-training for every new instance of physical parameters and shape of the domain.