This paper addresses the problem of generating textures for 3D mesh assets. Existing approaches often rely on image diffusion models to generate multi-view image observations, which are then transformed onto the mesh surface to produce a single texture. However, due to the gap between multi-view images and 3D space, such process is susceptible to arange of issues such as geometric inconsistencies, visibility occlusion, and baking artifacts. To overcome this problem, we propose a novel approach that directly generates texture on 3D meshes. Our approach leverages heat dissipation diffusion, which serves as an efficient operator that propagates features on the geometric surface of a mesh, while remaining insensitive to the specific layout of the wireframe. By integrating this technique into a generative diffusion pipeline, we significantly improve the efficiency of texture generation compared to existing texture generation methods. We term our approach DoubleDiffusion, as it combines heat dissipation diffusion with denoising diffusion to enable native generative learning on 3D mesh surfaces.
Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.