Symbolic Shock Sensor for Physics-Informed Mixture-of-Experts Surrogates in Transonic Aerodynamics
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The development of accurate surrogate models for the prediction of aerodynamic surface fields in the transonic regime remains challenging because shock waves introduce strong non-linearities and locally non-smooth behavior. Single-regressor models often smear discontinuities and degrade locally, and although regime-aware models, e.g. Mixture of Experts (MoE), can alleviate this problem, they typically rely on black-box gating or costly shock annotations. We propose a physics-informed and interpretable pipeline to predict surface pressure coefficient (Cp) (and optionally skin-friction components) on aircraft configurations under varying flow conditions, using only geometry and freestream inputs at inference. First, an offline discovery stage computes local spatial gradients from CFD snapshots and trains an autoencoder to embed the combined aerodynamic state into a low-dimensional latent space. A Gaussian mixture model clusters the latent representations to generate a pseudo shock mask without manual labeling. Second, symbolic regression identifies an analytic sensor function, which is calibrated with minimal trainable parameters and used as an interpretable gating signal. Finally, a MoE model is trained end-to-end with a weighted regression objective and a sensor-consistency loss, blending a smooth-flow expert and a shock-region expert. Experiments on a large transonic aircraft dataset show that the learned sensor consistently localizes shock regions in agreement with CFD patterns, and that regime-aware blending improves Cp reconstruction in shock-dominated areas, yielding sharper shock delineation and reduced localized errors compared with a single-regressor baseline.
