Generative Inverse Design with Abstention via Diagonal Flow Matching
This addresses a key bottleneck in generative inverse design for engineering applications like airfoil and gas turbine combustor design, offering more stable and reliable predictions.
The paper tackled the problem of unstable training in generative inverse design due to sensitivity to design parameter ordering and scaling, introducing Diagonal Flow Matching (Diag-CFM) which achieved order-of-magnitude improvements in round-trip accuracy over baselines across design dimensions up to 100.
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 order-of-magnitude improvements in round-trip accuracy over CFM and invertible neural network baselines across design dimensions up to $P{=}100$. 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, and an analytical benchmark with scalable design dimension.