KANGURA: Kolmogorov-Arnold Network-Based Geometry-Aware Learning with Unified Representation Attention for 3D Modeling of Complex Structures

TL;DR

The paper tackles the challenge of predicting and optimizing complex 3D geometries for manufacturability and performance, particularly in microbial fuel cell (MFC) anodes. It introduces KANGURA, a geometry-aware learning framework that combines Kolmogorov–Arnold Network (KAN) based function decomposition, geometry disentanglement in the spectral domain, and Unified Representation Attention (URA) to refine features. The approach processes point clouds via graph-based spectral representations, decomposes geometry into sharp and gentle components, and fuses information through URA to achieve state-of-the-art results on ModelNet40 (92.7% accuracy) and a real-world MFC dataset (97% accuracy). The work demonstrates significant potential for 3D structure modeling in advanced manufacturing and materials engineering, enabling faster design exploration and quality-driven optimization.

Abstract

Microbial Fuel Cells (MFCs) offer a promising pathway for sustainable energy generation by converting organic matter into electricity through microbial processes. A key factor influencing MFC performance is the anode structure, where design and material properties play a crucial role. Existing predictive models struggle to capture the complex geometric dependencies necessary to optimize these structures. To solve this problem, we propose KANGURA: Kolmogorov-Arnold Network-Based Geometry-Aware Learning with Unified Representation Attention. KANGURA introduces a new approach to three-dimensional (3D) machine learning modeling. It formulates prediction as a function decomposition problem, where Kolmogorov-Arnold Network (KAN)- based representation learning reconstructs geometric relationships without a conventional multi- layer perceptron (MLP). To refine spatial understanding, geometry-disentangled representation learning separates structural variations into interpretable components, while unified attention mechanisms dynamically enhance critical geometric regions. Experimental results demonstrate that KANGURA outperforms over 15 state-of-the-art (SOTA) models on the ModelNet40 benchmark dataset, achieving 92.7% accuracy, and excels in a real-world MFC anode structure problem with 97% accuracy. This establishes KANGURA as a robust framework for 3D geometric modeling, unlocking new possibilities for optimizing complex structures in advanced manufacturing and quality-driven engineering applications.

Figures (6)

• Figure 1: Illustration of the manufacturability classification process for 3D designs. Panel (a) shows manufacturable designs with feasible geometries. Panel (b) displays non-manufacturable designs with impractical features. Panel (c) demonstrates the testing phase, where the trained model is applied to predict the manufacturability of new designs.
• Figure 2: 3D visualizations of additional manufacturable and non-manufacturable designs, highlighting the internal structure of each object. Panels (a), (b), and (c) represent manufacturable designs, where the internal geometries are feasible for production. Panels (d), (e), and (f) display non-manufacturable designs, characterized by impractical internal features that prevent physical fabrication.
• Figure 2: Comparison of different models on ModelNet40 benchmark dataset
• Figure 3: Multi-view point cloud visualizations of 3D designs used for manufacturability classification. Panels (a)–(c) show manufacturable designs with feasible internal geometries. Panels (d)–(f) illustrate non-manufacturable designs featuring impractical structural configurations that restrict fabrication.
• Figure 4: Flowchart of the KANGURA