Domain-agnostic AI-based surrogate models: Transient flow prediction with domain-size and geometry invariance

A major challenge for machine-learning-based surrogate models is to generalise to geometries and domain sizes that differ from those used during training. Here, we propose DIGIT, a Domain-Size Invariant and Geometry Invariant surrogate model for Transient flows, with promising generalisation abilities. The DIGIT surrogate is based on a U-Net consisting entirely of convolutional layers, allowing the network to be applied to domains of arbitrary size. Furthermore, the architecture is tailored by selecting the kernel size and stride in such a way that a domain decomposition strategy is embedded within the network, encouraging the learning of local flow features. To enable the propagation of information across the domain within a single time step, which is needed to ensure satisfaction of the continuity equation as well as the transport of momentum, we introduce smoothing layers in the U-Net that couple neighbouring subdomains and promote global consistency of the solution. Boundary conditions and geometry constraints are enforced through an implicit scheme, which, alongside rollout training, adds to the accuracy and stability of the approach. The proposed method is demonstrated on a 2D incompressible Navier–Stokes test case, involving chaotic flow past buildings with varying domain sizes and geometry configurations. Once trained, we demonstrate that the DIGIT surrogate model is domain agnostic by its ability to generalise to unseen and substantially larger computational domains as well as unseen geometries without the need for retraining. Finally, we apply the same DIGIT model to a standard benchmark problem, flow past a cylinder, to demonstrate its generality.