Generative Inverse Design with Abstention via Diagonal Flow Matching
arXiv:2603.15925v1 Announce Type: new Abstract: 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 cap
arXiv:2603.15925v1 Announce Type: new Abstract: 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.
Executive Summary
This article presents Diagonal Flow Matching (Diag-CFM), a novel approach to generative inverse design, addressing the limitations of standard conditional flow matching (CFM) in handling arbitrary ordering and scaling of design parameters. Diag-CFM leverages a zero-anchoring strategy to pair design coordinates with noise and labels with zero, ensuring provable invariance to coordinate permutations. The proposed method demonstrates significant improvements in round-trip accuracy over CFM and invertible neural network baselines across various design dimensions. Additionally, the authors develop two architecture-intrinsic uncertainty metrics, enabling practical capabilities such as selecting the best candidate, abstaining from unreliable predictions, and detecting out-of-distribution targets. The approach is validated on three benchmarks, showcasing its potential in solving real-world design challenges.
Key Points
- ▸ Diagonal Flow Matching (Diag-CFM) is introduced to address limitations of standard CFM in handling arbitrary ordering and scaling.
- ▸ Diag-CFM uses a zero-anchoring strategy to pair design coordinates with noise and labels with zero, ensuring invariance to coordinate permutations.
- ▸ The proposed method demonstrates significant improvements in round-trip accuracy over CFM and invertible neural network baselines.
- ▸ Two architecture-intrinsic uncertainty metrics are developed, enabling practical capabilities such as selecting the best candidate and detecting out-of-distribution targets.
Merits
Improved Accuracy
Diag-CFM demonstrates significant improvements in round-trip accuracy over CFM and invertible neural network baselines, making it a more reliable approach for generative inverse design.
Invariance to Coordinate Permutations
The zero-anchoring strategy used in Diag-CFM ensures provable invariance to coordinate permutations, addressing a major limitation of standard CFM.
Practical Capabilities
The two architecture-intrinsic uncertainty metrics developed in this article enable practical capabilities such as selecting the best candidate, abstaining from unreliable predictions, and detecting out-of-distribution targets.
Demerits
Computational Complexity
The proposed method may require significant computational resources, particularly for high-dimensional design spaces, which could be a limitation for real-world applications.
Limited Generalizability
The method's performance may not generalize well to other design domains or applications, requiring further evaluation and adaptation.
Expert Commentary
The article presents a novel approach to generative inverse design, addressing a significant limitation of standard CFM. The proposed method demonstrates impressive improvements in round-trip accuracy and provides practical capabilities for uncertainty quantification. However, the computational complexity and limited generalizability of the method require further investigation. The article's findings have significant implications for real-world design challenges and policy decisions related to design processes. The proposed method has the potential to be a game-changer in the field of generative design, and its development and application warrant further research and exploration.
Recommendations
- ✓ Future research should focus on investigating the computational complexity of the proposed method and exploring methods to reduce it.
- ✓ The developed uncertainty metrics should be further evaluated and adapted for other design domains and applications.