Geometric deep learning for surrogate modeling
Surrogate models are playing an increasingly strategic role in modern engineering workflows, enabling faster design iterations and reducing computational costs. In our industrial experience, we have developed robust and reliable solutions that effectively address geometrically parametrized problems, where variability arises from changes in the underlying geometry. Building on these results, we now move toward the next generation of surrogate modeling techniques. In this context, deep geometric learning represents a promising and innovative direction. Our latest workflow is specifically designed to overcome the main limitations of classical approaches based on Linear Encoders like Proper Orthogonal Decomposition (POD). In standard POD-based pipelines, all solution fields must be defined on a common mesh, leading to significant preprocessing efforts and limiting flexibility in real-world applications.
Our approach removes this constraint entirely. By leveraging deep learning models that operate directly on point clouds, each geometry can be handled in its native discretization, without requiring mesh alignment or explicit parametrization. This is particularly relevant for industrial applications, where numerical solutions are often computed on non-consistent meshes for each configuration, and a well-defined parametrization is either unavailable or difficult to establish. As a result, the proposed methodology significantly simplifies the overall workflow and improves scalability across complex and heterogeneous datasets, enabling a straightforward setup of the surrogate modeling pipeline and substantially reducing preprocessing overhead. To demonstrate the effectiveness and practical viability of this approach, we consider the DrivAer test case. This is a fully parametrized benchmark geometry without topological variations and is therefore particularly suitable for a direct comparison between the classical POD-based reduced-order modeling workflow and the proposed deep geometric learning framework.
