Shift and flip invariant CNNs for predicting laminar flow properties

The integration of machine learning into fluid dynamics has accelerated in recent years, driven by the proliferation of high-fidelity data and enhanced computational resources. Acting as efficient surrogate models for computationally intensive simulations, these data-driven approaches provide substantial benefits, particularly during the preliminary stages of design and optimization. Previous investigations have employed convolutional neural networks (CNNs) to predict thermo-fluid flow properties for a variety of channel geometries. These studies have largely relied on data augmentation techniques to handle geometric transformations. However, such augmentation strategies are often inefficient in capturing the inherent flip and shift invariances of flow channel data. In this study, we demonstrate that embedding these invariances directly into the model architecture not only enhances robustness but leads to superior performance while significantly reducing the number of parameters compared to their invariant-unaware counterparts. In particular, we introduce two novel architectures designed to alleviate the sensitivity of CNNs to periodic signal shifts and vertical flips. This approach allows the model to structurally address the geometric symmetries of the flow channel data, offering a more robust alternative to standard data augmentation.