Technology Category
Search and Optimization: Mixed Discrete/Continuous SearchHumans and AI: Game Design — Procedural Content Generation & StorytellingPlanning, Routing, and Scheduling: Replanning and Plan Repair
Towards Generative Design Using Optimal Transport for Shape Exploration and Solution Field Interpolation
🤖 AI Summary
Existing generative design methods suffer from strong data dependency, difficulty in extending to multi-physics scenarios, and low geometric-field coupling accuracy under large deformations. This paper proposes an optimal-transport-based generative design framework that integrates Wasserstein barycenters with Gaussian splatting to enable synchronized, mass-conserving interpolation of geometry and multi-physics fields (scalar and vector) on non-matching meshes and under large deformations. By transcending the limitations of static-mesh surrogate models, the method explicitly preserves localized physical features—such as stress concentrations—thereby significantly improving fidelity and physical consistency in design space exploration. Experimental results demonstrate the framework’s efficiency, robustness, and superiority across diverse scenarios. The approach establishes a new paradigm for high-fidelity, scalable generative design.
Technology Category
Application Category
📝 Abstract
Generative Design (GD) combines artificial intelligence (AI), physics-based modeling, and multi-objective optimization to autonomously explore and refine engineering designs. Despite its promise in aerospace, automotive, and other high-performance applications, current GD methods face critical challenges: AI approaches require large datasets and often struggle to generalize; topology optimization is computationally intensive and difficult to extend to multiphysics problems; and model order reduction for evolving geometries remains underdeveloped. To address these challenges, we introduce a unified, structure-preserving framework for GD based on optimal transport (OT), enabling simultaneous interpolation of complex geometries and their associated physical solution fields across evolving design spaces, even with non-matching meshes and substantial shape changes. This capability leverages Gaussian splatting to provide a continuous, mesh-independent representation of the solution and Wasserstein barycenters to enable smooth, mathematically ''mass''-preserving blending of geometries, offering a major advance over surrogate models tied to static meshes. Our framework efficiently interpolates positive scalar fields across arbitrarily shaped, evolving geometries without requiring identical mesh topology or dimensionality. OT also naturally preserves localized physical features -- such as stress concentrations or sharp gradients -- by conserving the spatial distribution of quantities, interpreted as ''mass'' in a mathematical sense, rather than averaging them, avoiding artificial smoothing. Preliminary extensions to signed and vector fields are presented. Representative test cases demonstrate enhanced efficiency, adaptability, and physical fidelity, establishing a foundation for future foundation-model-powered generative design workflows.
Problem
Research questions and friction points this paper is trying to address.
Interpolating complex geometries and physical fields across evolving design spaces with non-matching meshes
Addressing computational intensity and multiphysics limitations in current topology optimization methods
Preserving localized physical features during shape blending without artificial smoothing effects
Innovation
Methods, ideas, or system contributions that make the work stand out.
Optimal transport framework for shape and field interpolation
Gaussian splatting enables mesh-independent continuous representation
Wasserstein barycenters preserve physical features without smoothing
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