Conditional Flow Matching for ML-Based Inverse Design Problems
TL;DR
Comparing CFM against conditional Diffusion and cGAN across structural and thermal benchmarks from EngiBench under matched downstream optimization conditions supports CFM as a competitive warm-start prior for engineering inverse design, substantially reducing inference cost relative to the evaluated Diffusion baseline while matching or exceeding its optimization utility at a fraction of the sampling budget.
Abstract
Engineering inverse design is often limited by the high computational cost of iterative PDE-constrained solvers and their sensitivity to initialization. While Deep Generative Models (DGMs) offer a path toward real-time synthesis, current models involve a practical trade-off: Generative Adversarial Networks (GANs) provide rapid inference but can suffer from training instability and mode collapse, while Diffusion models are often stable and expressive but incur high sampling latency from iterative reverse-time integration. In this work, we integrate and evaluate Conditional Flow Matching (CFM) as a new generative model added to EngiOpt, comparing it against conditional Diffusion and cGAN across structural (beams2d) and thermal (heatconduction2d) benchmarks from EngiBench under matched downstream optimization conditions. Beyond standard distributional metrics, we prioritize optimization metrics — Cumulative Optimality Gap (COG) and Final Optimality Gap (FOG) — to measure each model's efficacy as a warm-start prior for gradient-based refinement. On the evaluated EngiOpt implementations and two EngiBench tasks, CFM achieves the lowest COG, MMD, and volume fraction deviation, as well as the lowest FOG on heatconduction2d. Constraint adherence is particularly telling: CFM stays within 0.4% and 1.0% of the volume fraction target on beams2d and heatconduction2d respectively, while the evaluated Diffusion baseline deviates by 5.5% and 12.1%. At Euler s = 16 (Number of Function Evaluations, NFE= 16), CFM achieves 54.0 samples/sec on beams2d — about 69× the measured throughput of the evaluated Diffusion baseline at NFE= 1000 under the same timing protocol — with no meaningful loss in optimization quality. These results support CFM as a competitive warm-start prior for engineering inverse design, substantially reducing inference cost relative to the evaluated Diffusion baseline while matching or exceeding its optimization utility at a fraction of the sampling budget.