Pareto-Optimal Hypersonic Vehicle Design with Canonical-Coordinate Neural Operator Surrogates Under Ablation-Driven Shape Change and Incidence Variation
Abstract
High-fidelity CFD is essential for coupled hypersonic aerodynamic and aerothermal phenomena, but its cost precludes multi-objective design optimization. We develop three DeepONet surrogates for two hypersonic configurations, unified by one device: the trunk receives coordinates in which the varying feature is held fixed. The first is a prescribed family of 37 spherically blunted tangent ogives, varied through ogive radius of curvature to span nose-tip ablation forebody change; no ablation is computed. A body-fitted canonical transformation maps every domain onto a common (s, eta) space, retaining physical coordinates for forces and heat transfer. A branch network predicts reduced coefficients and a Transolver trunk with Physics-Attention learns the spatial basis; a two-step strategy optimizes both jointly, orthonormalizes the basis by QR factorization, and trains a second-stage branch for unseen geometries. Surrogates cover density, pressure, velocity, temperatures, conductivities and species mass fractions. In leave-one-out tests, drag, mean and peak wall heat flux are recovered to 1.16%, 1.62% and 5.29%; a sweep of 1001 geometries gives a 200-design Pareto front trading 6.68% in drag for 4.42% in peak heating (a diagnostic, not an objective). The second is the 3D AEDC waverider at 29 angles of attack: static mesh, moving leading-edge shock. For surface quantities, the same construction predicts integrated heat load within 0.22% and force coefficients to errors below 2.6x10^-5; Pareto fronts identify angles of attack trading drag, lift and heating. For the volume field, a Cartesian trunk smears the shock; a frozen ShockNet supplies a shock-aligned coordinate and a hotspot-aware mixture of experts corrects the residual, recovering density to 12.28% relative L2 error at a held-out incidence (5.08x10^7 nodes). The 1001-design sweep takes about three minutes on a single CPU.
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BibTeX
@misc{shukla2026paretooptimal,
title = {{Pareto-Optimal Hypersonic Vehicle Design with Canonical-Coordinate Neural Operator Surrogates Under Ablation-Driven Shape Change and Incidence Variation}},
author = {Khemraj Shukla and Jeremy Redding and Luis Bravo and George Em Karniadakis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40731},
eprint = {2610.40731},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40731},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pareto-Optimal Hypersonic Vehicle Design with Canonical-Coordinate Neural Operator Surrogates Under Ablation-Driven Shape Change and Incidence Variation
AU - Khemraj Shukla
AU - Jeremy Redding
AU - Luis Bravo
AU - George Em Karniadakis
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40731
UR - https://arxiv.org/abs/2610.40731
AB - High-fidelity CFD is essential for coupled hypersonic aerodynamic and aerothermal phenomena, but its cost precludes multi-objective design optimization. We develop three DeepONet surrogates for two hypersonic configurations, unified by one device: the trunk receives coordinates in which the varying feature is held fixed. The first is a prescribed family of 37 spherically blunted tangent ogives, varied through ogive radius of curvature to span nose-tip ablation forebody change; no ablation is computed. A body-fitted canonical transformation maps every domain onto a common (s, eta) space, retaining physical coordinates for forces and heat transfer. A branch network predicts reduced coefficients and a Transolver trunk with Physics-Attention learns the spatial basis; a two-step strategy optimizes both jointly, orthonormalizes the basis by QR factorization, and trains a second-stage branch for unseen geometries. Surrogates cover density, pressure, velocity, temperatures, conductivities and species mass fractions. In leave-one-out tests, drag, mean and peak wall heat flux are recovered to 1.16%, 1.62% and 5.29%; a sweep of 1001 geometries gives a 200-design Pareto front trading 6.68% in drag for 4.42% in peak heating (a diagnostic, not an objective). The second is the 3D AEDC waverider at 29 angles of attack: static mesh, moving leading-edge shock. For surface quantities, the same construction predicts integrated heat load within 0.22% and force coefficients to errors below 2.6x10^-5; Pareto fronts identify angles of attack trading drag, lift and heating. For the volume field, a Cartesian trunk smears the shock; a frozen ShockNet supplies a shock-aligned coordinate and a hotspot-aware mixture of experts corrects the residual, recovering density to 12.28% relative L2 error at a held-out incidence (5.08x10^7 nodes). The 1001-design sweep takes about three minutes on a single CPU.
ER -