Machine learning (ML) provides a promising means to improve Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling, but efficiently enforcing realizability, or the non-negativity of turbulent kinetic energy, has remained a challenge. Current approaches rely on costly post-processing corrections or inexact penalty methods that can suffer from ill-conditioning and fail in out-of-distribution scenarios.Here, we introduce the first realizable tensor basis neural network (RTBNN) architecture that implicitly enforces realizability without eigendecomposition, extra hyperparameters, or penalty terms during training. First, a polar invariant map is constructed to provide a physically meaningful framework to represent realizability as a scaling problem instead of an eigenvalue constraint. This is used to develop an architecture that predicts the normalized anisotropy magnitude relative to its maximum realizable value. A proof-of-concept model was implemented and compared to the standard tensor basis neural network (TBNN) and realizability-informed (RI-TBNN) architectures using square duct data
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