Accurate machine learning-based subgrid-scale modelling requires neural network architectures that represent the turbulent energy cascade, rather than relying on assumed scale correlations embedded in the training data. In this work, we propose an encoder-decoder architecture to learn a structurally conditioned functional representation of subgrid-scale turbulence while retaining the Germano-Lilly formulation for the Smagorinsky coefficient \( \user2{C}_{\user2{s}} \) . The proposed closure replaces explicit test filtering, spatial averaging, and coefficient clipping with an implicit multi-scale representation learned by a wavelet-assisted encoder–decoder (WED) with skip connections. By encoding scale-aware features across multiple layers of neural networks, the model preserves large-scale coherence while adapting to local flow dynamics. A-priori and a-posteriori analyses are conducted for flow past a sphere at \( \user2{\mathcal{R}e}{\mathbf{ = 10}}^{{\mathbf{3}}} \) and \( {\mathbf{10}}^{{\mathbf{4}}} \) to quantify training data inconsistency and model performance relative to a deep ANN architecture. In a-priori tests, the proposed WED shows the best performance when the structural SGS stress was conditioned on the velocity-gradient tensor \( \user2{\mathcal{G}}_{{\user2{ij}}} \) and the resolved second moment \( \user2{\tau }_{{\user2{ij}}}^{\user2{\prime }} \) . In a-posteriori tests, the proposed WED exhibits the best performance relative to DNS and experimental data within the recirculation region, where the dynamic Smagorinsky model experiences pronounced spectral inconsistency in scale-similar stresses. The results highlight the importance of addressing spectral inconsistency arising from scale-similarity assumptions in dynamic SGS models and indicate that learning the underlying multi-scale energy cascade within a physics-guided Germano–Lilly framework provides a practical and robust closure strategy.
