Airfoil shape optimization via coherent Ising machine

TL;DR

This work proposes a comprehensive framework that translates airfoil shape optimization into hardware-compliant quadratic unconstrained binary optimization formulations, and introduces a block-diagonal scalarization strategy that compose trade-off scenarios into a single optimization.

Abstract

Airfoil shape optimization presents a challenge where classical solvers frequently struggle with computational efficiency and local minima. In the promising paradigm of quantum computing, the coherent Ising machine (CIM), a specialized physical solver, offers acceleration capabilities. However, its native discrete binary architecture restricts the application in aerodynamic design. To bridge this gap, we propose a comprehensive framework that translates airfoil shape optimization into hardware-compliant quadratic unconstrained binary optimization formulations. We integrate high-order response surface models via the Rosenberg order reduction, enabling the CIM to capture strong nonlinearities in the aerodynamic performance response. Furthermore, we introduce a block-diagonal scalarization strategy that compose trade-off scenarios into a single optimization. Validated on the NACA 4-digit airfoil series using CIM hardware with 615 spins, the framework successfully locates the global optimum with a computational speedup of three orders of magnitude compared to the classical simulated annealing. The parallel embedding capacity allows for the extraction of an entire optimal Pareto front in a single hardware execution. This work demonstrates a viable, quantum-enhanced paradigm for engineering optimization.

Figures (6)

• Figure 1: End-to-end airfoil shape optimization workflow using CIM. The process bridges classical aerodynamic simulation with quantum-enhanced optimization, progressing from data generation and surrogate modeling to binary formulation, hardware embedding, and final design decoding.
• Figure 1: Analysis of solution candidates and spin overhead across different discretization precisions. (a) Comparison of discretization candidates under 3- and 6-bit precisions. (b) The spin counts for discretization bits $K=$ 3, 4, 5, and 6. The total required spins are decomposed into the logical, QUBO auxiliary, and physical auxiliary spins.
• Figure 2: Sampling, construction, and validation of RSMs for the NACA 4-digit airfoil series. (a) 3D visualization of the design space and sampling points, colored by the lift-to-drag ratio $C_L/C_D$. (b, c) Volumetric representation of the second- and fourth-order RSMs displayed with a partial cutaway for interior visualization. (d, e) Parity plots of predicted vs. true values of $C_L/C_D$. (f) 2D cross-section at fixed camber parameters $A=6$ and $B=5$, showing the dependence of $C_L/C_D$ on thickness $T$.
• Figure 3: Validation of optimization fidelity and computational efficiency on the baseline case with $Re=3.0\times 10^6$ and $\alpha = 5.0^\circ$. (a) Geometric profiles of the optimized airfoils identified by the CIM (red), overlaid with results from SA (light blue), GD (dark blue), and the ground truth BF (black). Thin gray lines represent a subset of the airfoil sample space. (b) Temporal convergence comparing between the CIM and SA. The optimization trajectories of the CIM (red line) and the SA baseline (blue line) is tracked via the normalized Hamiltonian gap $\Delta \tilde{H}(t)$. The shaded regions denote the standard deviation across five independent runs, and vertical dashed lines mark the TTTs.
• Figure 4: Optimization results for $C_L/C_D$ of the NACA 4-digit airfoils with $A = 6$ and $B = 4$ utilizing second- and fourth-order RSMs.