Variational Rank Reduction Autoencoders for Generative Thermal Design
This work addresses thermal design problems for engineering applications, offering an incremental improvement by integrating structured latent representations with operator networks.
The paper tackled the challenges of generative thermal design, such as high computational costs and unstructured latent spaces in autoencoders, by proposing a hybrid framework combining Variational Rank-Reduction Autoencoders with Deep Operator Networks, which improved geometric reconstruction and gradient prediction accuracy while enhancing inference efficiency compared to traditional solvers.
Generative thermal design for complex geometries is fundamental in many areas of engineering, yet it faces two main challenges: the high computational cost of high-fidelity simulations and the limitations of conventional generative models. Approaches such as autoencoders (AEs) and variational autoencoders (VAEs) often produce unstructured latent spaces with discontinuities, which restricts their capacity to explore designs and generate physically consistent solutions. To address these limitations, we propose a hybrid framework that combines Variational Rank-Reduction Autoencoders (VRRAEs) with Deep Operator Networks (DeepONets). The VRRAE introduces a truncated SVD within the latent space, leading to continuous, interpretable, and well-structured representations that mitigate posterior collapse and improve geometric reconstruction. The DeepONet then exploits this compact latent encoding in its branch network, together with spatial coordinates in the trunk network, to predict temperature gradients efficiently and accurately. This hybrid approach not only enhances the quality of generated geometries and the accuracy of gradient prediction, but also provides a substantial advantage in inference efficiency compared to traditional numerical solvers. Overall, the study underscores the importance of structured latent representations for operator learning and highlights the potential of combining generative models and operator networks in thermal design and broader engineering applications.