Previouswork onneural 3Dreconstruction demonstrated benefits, butalso limitations, ofpoint cloud, voxel, surface mesh, and implicit function representations. Unlike existing volumetric approaches,DEFTET optimizes for both vertex placement and occupancy, and is differentiable with respect to standard 3D reconstruction lossfunctions.

Gradient-based optimization of engineering designs is limited by non-differentiable components in the typical computer-aided engineering (CAE) workflow, which calculates performance metrics from design parameters. While gradient-based methods could provide noticeable speed-ups in high-dimensional design spaces, codes for meshing, physical simulations, and other common components are not differentiable even if the math or physics underneath them is. We propose replacing non-differentiable pipeline components with surrogate models which are inherently differentiable. Using a toy example of aerodynamic shape optimization, we demonstrate an end-to-end differentiable pipeline where a 3D U-Net full-field surrogate replaces both meshing and simulation steps by training it on the mapping between the signed distance field (SDF) of the shape and the fields of interest. This approach enables gradient-based shape optimization without the need for differentiable solvers, which can be useful in situations where adjoint methods are unavailable and/or hard to implement.

Alzheimer's disease (AD) is a major neurodegenerative condition that affects millions around the world. As one of the main biomarkers in the AD diagnosis procedure, brain amyloid positivity is typically identified by positron emission tomography (PET), which is costly and invasive. Brain structural magnetic resonance imaging (sMRI) may provide a safer and more convenient solution for the AD diagnosis. Recent advances in geometric deep learning have facilitated sMRI analysis and early diagnosis of AD. However, determining AD pathology, such as brain amyloid deposition, in preclinical stage remains challenging, as less significant morphological changes can be observed. As a result, few AD classification models are generalizable to the brain amyloid positivity classification task. Blood-based biomarkers (BBBMs), on the other hand, have recently achieved remarkable success in predicting brain amyloid positivity and identifying individuals with high risk of being brain amyloid positive. However, individuals in medium risk group still require gold standard tests such as Amyloid PET for further evaluation. Inspired by the recent success of transformer architectures, we propose a geometric deep learning model based on transformer that is both scalable and robust to variations in input volumetric mesh size. Our work introduced a novel tokenization scheme for tetrahedral meshes, incorporating anatomical landmarks generated by a pre-trained Gaussian process model. Our model achieved superior classification performance in AD classification task. In addition, we showed that the model was also generalizable to the brain amyloid positivity prediction with individuals in the medium risk class, where BM alone cannot achieve a clear classification. Our work may enrich geometric deep learning research and improve AD diagnosis accuracy without using expensive and invasive PET scans.

Skinning is a popular way to rig and deform characters for animation, to compute reduced-order simulations, and to define features for geometry processing. Methods built on skinning rely on weight functions that distribute the influence of each degree of freedom across the mesh. Automatic skinning methods generate these weight functions with minimal user input, usually by solving a variational problem on a mesh whose boundary is the skinned surface. This formulation necessitates tetrahedralizing the volume inside the surface, which brings with it meshing artifacts, the possibility of tetrahedralization failure, and the impossibility of generating weights for surfaces that are not closed. We introduce a mesh-free and robust automatic skinning method that generates high-quality skinning weights comparable to the current state of the art without volumetric meshes. Our method reliably works even on open surfaces and triangle soups where current methods fail. We achieve this through the use of a Lagrangian representation for skinning weights, which circumvents the need for finite elements while optimizing the biharmonic energy.

This study introduces a two-scale Graph Neural Operator (GNO), namely, LatticeGraphNet (LGN), designed as a surrogate model for costly nonlinear finite-element simulations of three-dimensional latticed parts and structures. LGN has two networks: LGN-i, learning the reduced dynamics of lattices, and LGN-ii, learning the mapping from the reduced representation onto the tetrahedral mesh. LGN can predict deformation for arbitrary lattices, therefore the name operator. Our approach significantly reduces inference time while maintaining high accuracy for unseen simulations, establishing the use of GNOs as efficient surrogate models for evaluating mechanical responses of lattices and structures.

Machine learning (ML) is becoming increasingly popular for predicting material properties to accelerate materials discovery. Because material properties are strongly affected by its crystal structure, a key issue is converting the crystal structure into the features for input to the ML model. Currently, the most common method is to convert the crystal structure into a graph and predicting its properties using a graph neural network (GNN). Some GNN models, such as crystal graph convolutional neural network (CGCNN) and atomistic line graph neural network (ALIGNN), have achieved highly accurate predictions of material properties. Despite these successes, using a graph to represent a crystal structure has the notable limitation of losing the crystal structure's three-dimensional (3D) information. In this work, we propose DeepCrysTet, a novel deep learning approach for predicting material properties, which uses crystal structures represented as a 3D tetrahedral mesh generated by Delaunay tetrahedralization. DeepCrysTet provides a useful framework that includes a 3D mesh generation method, mesh-based feature design, and neural network design. The experimental results using the Materials Project dataset show that DeepCrysTet significantly outperforms existing GNN models in classifying crystal structures and achieves state-of-the-art performance in predicting elastic properties.

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry, generative modeling, and inverse physics. Existing implementations adapt classic isosurface extraction algorithms like Marching Cubes or Dual Contouring; these techniques were designed to extract meshes from fixed, known fields, and in the optimization setting they lack the degrees of freedom to represent high-quality feature-preserving meshes, or suffer from numerical instabilities. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives. Our main insight is to introduce additional carefully-chosen parameters into the representation, which allow local flexible adjustments to the extracted mesh geometry and connectivity. These parameters are updated along with the underlying scalar field via automatic differentiation when optimizing for a downstream task. We base our extraction scheme on Dual Marching Cubes for improved topological properties, and present extensions to optionally generate tetrahedral and hierarchically-adaptive meshes. Extensive experiments validate FlexiCubes on both synthetic benchmarks and real-world applications, showing that it offers significant improvements in mesh quality and geometric fidelity.

We present TetGAN, a convolutional neural network designed to generate tetrahedral meshes. We represent shapes using an irregular tetrahedral grid which encodes an occupancy and displacement field. Our formulation enables defining tetrahedral convolution, pooling, and upsampling operations to synthesize explicit mesh connectivity with variable topological genus. The proposed neural network layers learn deep features over each tetrahedron and learn to extract patterns within spatial regions across multiple scales. We illustrate the capabilities of our technique to encode tetrahedral meshes into a semantically meaningful latent-space which can be used for shape editing and synthesis. Our project page is at https://threedle.github.io/tetGAN/.

Deep generative models have shown success in generating 3D shapes with different representations. In this work, we propose Neural Volumetric Mesh Generator (NVMG), which can generate novel and high-quality volumetric meshes. Unlike the previous 3D generative model for point cloud, voxel, and implicit surface, the volumetric mesh representation is a ready-to-use representation in industry with details on both the surface and interior. Generating this such highly-structured data thus brings a significant challenge. We first propose a diffusion-based generative model to tackle this problem by generating voxelized shapes with close-to-reality outlines and structures. We can simply obtain a tetrahedral mesh as a template with the voxelized shape. Further, we use a voxel-conditional neural network to predict the smooth implicit surface conditioned on the voxels, and progressively project the tetrahedral mesh to the predicted surface under regularizations. The regularization terms are carefully designed so that they can (1) get rid of the defects like flipping and high distortion; (2) force the regularity of the interior and surface structure during the deformation procedure for a high-quality final mesh. As shown in the experiments, our pipeline can generate high-quality artifact-free volumetric and surface meshes from random noise or a reference image without any postprocessing. Compared with the state-of-the-art voxel-to-mesh deformation method, we show more robustness and better performance when taking generated voxels as input. How to automatically create high-quality new 3D contents that are accessible and editable is a key problem in visual computing.