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1. Enumeration and Identification of Unique 3D Spatial Topologies of Interconnected Engineering Systems Using Spatial Graphs

   https://doi.org/10.1115/1.4062978  

   Peddada, Satya_R T; Dunfield, Nathan M; Zeidner, Lawrence E; Givans, Zane R; James, Kai A; Allison, James T (October 2023, Journal of Mechanical Design)

   Systematic enumeration and identification of unique 3D spatial topologies (STs) of complex engineering systems (such as automotive cooling systems, electric power trains, satellites, and aero-engines) are essential to navigation of these expansive design spaces with the goal of identifying new spatial configurations that can satisfy challenging system requirements. However, efficient navigation through discrete 3D ST options is a very challenging problem due to its combinatorial nature and can quickly exceed human cognitive abilities at even moderate complexity levels. This article presents a new, efficient, and scalable design framework that leverages mathematical spatial graph theory to represent, enumerate, and identify distinctive 3D topological classes for a generic 3D engineering system, given its system architecture (SA)—its components and their interconnections. First, spatial graph diagrams (SGDs) are generated for a given SA from zero to a specified maximum number of interconnect crossings. Then, corresponding Yamada polynomials for all the planar SGDs are generated. SGDs are categorized into topological classes, each of which shares a unique Yamada polynomial. Finally, within each topological class, 3D geometric models are generated using the SGDs having different numbers of interconnect crossings. Selected case studies are presented to illustrate the different features of our proposed framework, including an industrial engineering design application: ST enumeration of a 3D automotive fuel cell cooling system (AFCS). Design guidelines are also provided for practicing engineers to aid the application of this framework to different types of real-world problems such as configuration design and spatial packaging optimization. 

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2. Learning and Visualizing Localized Geometric Features Using 3D-CNN: An Application to Manufacturability Analysis of Drilled Holes

   Ghadai, Sambit; Balu, Aditya; Krishnamurthy, Adarsh; Sarkar, Soumik (January 2017, NIPS Symposium on Interpretable Machine Learning)

   3D Convolutional Neural Networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. However, interpreting the decision making process of these 3D-CNNs is still an infeasible task. In this paper, we present a unique 3D-CNN based Gradient-weighted Class Activation Mapping method (3D-GradCAM) for visual explanations of the distinct local geometric features of interest within an object. To enable efficient learning of 3D geometries, we augment the voxel data with surface normals of the object boundary. We then train a 3D-CNN with this augmented data and identify the local features critical for decision-making using 3D GradCAM. An application of this feature identification framework is to recognize difficult-to-manufacture drilled hole features in a complex CAD geometry. The framework can be extended to identify difficult-to-manufacture features at multiple spatial scales leading to a real-time design for manufacturability decision support system. 

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3. Earth Imagery Segmentation on Terrain Surface with Limited Training Labels: A Semi-supervised Approach based on Physics-Guided Graph Co-Training

   https://doi.org/10.1145/3481043  

   He, Wenchong; Sainju, Arpan Man; Jiang, Zhe; Yan, Da; Zhou, Yang (April 2022, ACM Transactions on Intelligent Systems and Technology)

   Given earth imagery with spectral features on a terrain surface, this paper studies surface segmentation based on both explanatory features and surface topology. The problem is important in many spatial and spatiotemporal applications such as flood extent mapping in hydrology. The problem is uniquely challenging for several reasons: first, the size of earth imagery on a terrain surface is often much larger than the input of popular deep convolutional neural networks; second, there exists topological structure dependency between pixel classes on the surface, and such dependency can follow an unknown and non-linear distribution; third, there are often limited training labels. Existing methods for earth imagery segmentation often divide the imagery into patches and consider the elevation as an additional feature channel. These methods do not fully incorporate the spatial topological structural constraint within and across surface patches and thus often show poor results, especially when training labels are limited. Existing methods on semi-supervised and unsupervised learning for earth imagery often focus on learning representation without explicitly incorporating surface topology. In contrast, we propose a novel framework that explicitly models the topological skeleton of a terrain surface with a contour tree from computational topology, which is guided by the physical constraint (e.g., water flow direction on terrains). Our framework consists of two neural networks: a convolutional neural network (CNN) to learn spatial contextual features on a 2D image grid, and a graph neural network (GNN) to learn the statistical distribution of physics-guided spatial topological dependency on the contour tree. The two models are co-trained via variational EM. Evaluations on the real-world flood mapping datasets show that the proposed models outperform baseline methods in classification accuracy, especially when training labels are limited. 

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4. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for Alzheimer’s disease

   https://doi.org/10.1038/s41467-022-35233-1  

   Zhang, Xinyi; Wang, Xiao; Shivashankar, G_V; Uhler, Caroline (December 2022, Nature Communications)

   Abstract Tissue development and disease lead to changes in cellular organization, nuclear morphology, and gene expression, which can be jointly measured by spatial transcriptomic technologies. However, methods for jointly analyzing the different spatial data modalities in 3D are still lacking. We present a computational framework to integrate Spatial Transcriptomic data using over-parameterized graph-based Autoencoders with Chromatin Imaging data (STACI) to identify molecular and functional alterations in tissues. STACI incorporates multiple modalities in a single representation for downstream tasks, enables the prediction of spatial transcriptomic data from nuclear images in unseen tissue sections, and provides built-in batch correction of gene expression and tissue morphology through over-parameterization. We apply STACI to analyze the spatio-temporal progression of Alzheimer’s disease and identify the associated nuclear morphometric and coupled gene expression features. Collectively, we demonstrate the importance of characterizing disease progression by integrating multiple data modalities and its potential for the discovery of disease biomarkers. 

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5. Surface-Toolpath Twins of Shell Components in 3D Concrete Printing for Optimized Buildability and Surface Quality

   ZHI, Y; AKBARZADEH, M (October 2025, Proceedings of the IASS Annual Symposium 2025)

   Gerardo_Oliva, J; Ignacio_del_Cueto, J; Drago, E (Ed.)

   This paper directly links the abstract geometry of structural form-finding to the fabrication-aware design of discrete shells and spatial structures for 3D concrete printing through a bidirectional approach, where it creates surface-toolpath twins for the components, optimizing the buildability of the parts and their surface quality. The design-to-production process of efficient structural systems for 3D printing is often a top-down unidirectional process involving form-finding, segmentation, and slicing, where results face printability challenges due to incompatibility between the initial geometry and the printing system, as well as material constraints. We introduce surface-toolpath twins that can be interconverted and synchronized through efficient slicing and surface reconstruction algorithms to allow the combination of optimizations and modifications on either part of the twin in flexible orders. We provide two core methods for fabrication rationalization: (1) global buildability optimization on the surface mesh by normal-driven shape stylization and (2) local surface quality optimization on toolpath curves through intra-layer iterative adjustments. The result is a bidirectional design-to-production process where one can plug and play different form-finding results, assess and optimize their fabrication schemes, or leverage knowledge in fabrication design, model toolpath curves as sections, reconstruct surfaces, and merge them into form-finding and segmentation in an inverse way. The proposed framework enables the integration of form-finding expertise with fabrication-oriented design, allowing the realization of spatial shell structures with complex topologies or extreme geometrical features through 3D concrete printing. 

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