Generative Design of a Gas Turbine Combustor Using Invertible Neural Networks

Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labels with design parameters, exhibits strong sensitivity to their arbitrary ordering and scaling, leading to unstable training. We introduce Diagonal Flow Matching (Diag--CFM), which resolves this through a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning problem provably invariant to coordinate permutations. This yields substantially lower round-trip error than CFM and invertible neural network baselines across design dimensions up to $P{=}784$, including order-of-magnitude gains on several benchmarks. We develop two architecture-intrinsic uncertainty metrics, Zero-Deviation and Self-Consistency, that enable three practical capabilities: selecting the best candidate among multiple generations, abstaining from unreliable predictions, and detecting out-of-distribution targets; consistently outperforming ensemble and general-purpose alternatives across all tasks. We validate on airfoil, gas turbine combustor, scalable analytical benchmarks, a photonics inverse-design task, and an image-statistics benchmark.

AI is increasingly used to accelerate engineering design by improving decision-making and shortening iteration cycles. Application to marine propeller design, however, remains challenging due to scarce training data and the lack of widely available pretrained models. We address this gap with a physics-based data generation pipeline and a generative-AI framework for direct performance-to-design generation tailored to marine propellers. First, we build a database of over 20,000 four- and five-bladed propeller geometries, each accompanied by simulated open-water performance curves. On top of this dataset, we develop a three-module design framework: (1) A Conditional Generation Model that proposes candidate geometries conditioned on design specifications such as target thrust, power, and diameter. (2) A Performance Prediction Model, implemented as a neural-network surrogate, that predicts thrust, torque, and efficiency in milliseconds, enabling rapid evaluation of generated designs. (3) A design refinement stage that applies evolutionary optimization to enforce practical constraints such as required thrust under power limits and bounds on blade-area ratio and thickness. Experimental results over a range of operating conditions show that the framework can generate hydrodynamically plausible propeller designs that match prescribed performance targets while substantially reducing design-iteration time relative to the traditional expert-guided refinement. Latent diffusion-based generator produces more diverse designs under the same conditions than the conditional variational autoencoder, suggesting a stronger capacity for design-space exploration with diffusion models. By coupling physics-based data synthesis with modular AI models, the proposed approach streamlines the propeller design cycle and reduces reliance on expensive high-fidelity simulations to final validation stages.

Engineering inverse design is often limited by the high computational cost of iterative solvers for optimization problems constrained by partial differential equations (PDEs) and by their sensitivity to initialization. Deep generative models can produce candidate designs without rerunning the simulator at inference time. Generative adversarial networks (GANs) sample in one forward pass, whereas diffusion models require iterative reverse-time integration. In this work, we add conditional flow matching (CFM) to EngiOpt and compare it with a conditional diffusion model and a conditional generative adversarial network (cGAN) on structural (beams2d) and thermal (heatconduction2d) benchmarks from EngiBench using the same downstream optimization protocol. We use cumulative optimality gap (COG) and final optimality gap (FOG) as the primary metrics for evaluating the generated designs as warm starts for gradient-based refinement. On the evaluated EngiOpt implementations and two EngiBench tasks, CFM achieves the lowest measured COG, FOG, maximum mean discrepancy (MMD), and volume-fraction deviation on both tasks. CFM has mean volume-fraction deviations of 0.4% and 1.0% on beams2d and heatconduction2d, respectively, compared with 3.8% and 11.2% for diffusion. At Euler s = 16, CFM achieves 53.2 samples/s on beams2d, about 66 times the measured throughput of the evaluated diffusion baseline using 1000 network evaluations under the same timing protocol, with COG 1.182 +/- 3.126, compared with 1.173 +/- 3.100 for Euler s = 32. Across the two tasks, CFM produces warm starts with lower measured COG than both baselines and uses fewer network evaluations than diffusion.