Interpretable discovery of anisotropic dissipation limiters for hypersonic flows via flow-aligned spatiotemporal graph attention and symbolic distillation

The Roe scheme is widely used for compressible-flow simulation, but its accuracy and robustness hinge on numerical-dissipation control. Existing entropy fixes and dissipation corrections are largely heuristic and can fail for complex shock–shear interactions, while data-driven models are often black boxes with nontrivial inference cost. We introduce a discovery pipeline that combines a flow-aligned spatiotemporal graph attention network (Flow-Aligned ST-GAT) with symbolic regression to obtain explicit anisotropic dissipation limiters that can be deployed without online neural-network inference. As a teacher model, Flow-Aligned ST-GAT embeds local velocity vectors and pressure gradients into anisotropic attention, enabling it to differentiate shock-normal and shear-layer-tangential dynamics and to mitigate spurious oscillations via temporal feature learning. The learned face-based limiter fields are then distilled into closed-form algebraic limiters through sparsity-constrained symbolic regression, which can be plugged directly into conventional solvers. Tests on representative benchmarks and additional out-of-distribution configurations involving unseen Riemann states, grid rotation, grid refinement, oblique shocks, held-out hypersonic-cylinder configurations, and a new shock-dominated geometry show that the data-distilled limiter suppresses carbuncle-like artifacts, preserves contact and vortical structures, and transfers stably beyond the configurations used for training. The proposed framework provides a practical route to interpretable and optimized dissipation control within the considered two-dimensional inviscid compressible-flow setting. Rather than claiming a completely new physical law, the resulting expression can be interpreted as a data-distilled, Roe-compatible generalization of classical shock/vortex sensors, combining compression-selective dissipation, vortex shielding, and pressure-gradient compensation within the Roe–Harten entropy-fix framework.