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A unified subgrid-scale (SGS) and wall model for large-eddy simulation (LES) is proposed by devising the flow as a collection of building blocks that enables the prediction of the eddy viscosity. The core assumption of the model is that simple canonical flows contain the essential physics to provide accurate predictions of the SGS tensor in more complex flows. The model is constructed to predict zero-pressure-gradient wall-bounded turbulence, adverse pressure gradient effects, separation and laminar flow. The approach is implemented using a Bayesian classifier, which identifies the contribution of each building block in the flow, and a neural-network-based predictor, which estimates the eddy viscosity based on the building-block units. The training data are directly obtained from wall-modeled LES with an exact SGS/wall model for the mean quantities to guarantee consistency with the numerical discretization. The model is validated in canonical flows and the NASA High-Lift Common Research Model and shown to improve the predictions with respect to current modeling approaches.