Trajectory-Aware Flow Matching for Topology Optimisation

Topology optimisation (TO) often requires repeated finite element analysis and sensitivity-based material updates, which can be costly when multiple candidate designs are needed under varying physical and design conditions. Generative TO offers a route to rapid design exploration, but existing models may rely on adversarial training, long reverse-diffusion sampling, or external guidance to maintain structural feasibility and physical consistency. This study develops a flow matching-based topology optimisation (FMTO) framework for conditional topology generation. Linear FMTO is first formulated as an endpoint-based baseline by interpolating between a Gaussian source field and the BESO reference topology. To introduce mechanically meaningful intermediate states, a trajectory-aware FMTO formulation is proposed, where volume-fraction-indexed BESO states are used to construct the probability path and target velocity field. This incorporates physics-guided optimisation history into generative flow learning without adding inference-time optimisation. A path--velocity mismatch analysis explains why moderate trajectory weighting can improve generation stability, whereas excessive guidance may over-constrain the learned transport. Numerical examples show that FMTO generates diverse topology candidates with improved compliance-related performance, volume-fraction satisfaction, topology fidelity, and substantially fewer sampling steps than a diffusion-based baseline. Under limited training data, trajectory-aware FMTO achieves the best overall performance with a moderate trajectory weight. Studies on trajectory-anchor density and three-dimensional topology generation further demonstrate the influence of path design and the applicability of the proposed framework beyond two-dimensional problems.

DeepJEB++: Foundation Model-Driven Large-Scale 3D Engineering Dataset via 2D Latent Space Augmentation

Data-driven engineering design is constrained by the lack of large-scale 3D datasets that pair geometry with physics-based performance labels. In particular, existing 3D data augmentation techniques have limitations in preserving subtle and diverse geometric variations, and it remains difficult to automate the subsequent simulation-labeling process, where boundary conditions vary depending on the generated geometry. We present DeepJEB++, a foundation-model-driven data-augmentation framework that expands a small seed set of jet engine brackets into a large, simulation-labeled 3D dataset under constrained resources. Our key idea is to augment in the data-rich 2D latent space, then transfer to 3D. In Stage 1, we fine-tune a pretrained 2D latent diffusion model on multi-view renders and synthesize novel views by latent interpolation, retaining manufacturable designs through a vision-language-model (VLM) quality filter. In Stage 2, the validated images are lifted to 3D meshes by a domain-adapted generative foundation model. In Stage 3, an automated pipeline recognizes the load and bolt interfaces on each mesh and assigns finite-element labels -- mass, stress, and displacement -- without manual intervention. We assess augmentation quality along three intrinsic axes: manufacturability, label fidelity against the SimJEB ground truth, and distributional consistency. Starting from fewer than 400 seed designs, DeepJEB++ yields 15,360 simulation-labeled 3D brackets -- a 40x expansion -- using a single GPU per stage. The dataset will be made publicly available to support reproducible engineering-AI research.