Yongjie Jessica Zhang

Hua Tong, Yongjie Jessica Zhang

Conforming hex meshes are widely regarded as an effective computational domain for simulation because of their nice numerical properties, yet automatically decomposing a general 3D volume into a conforming hex mesh remains a formidable challenge. Among existing approaches, methods that construct an adaptive Cartesian grid and subsequently convert it into a conforming mesh stand out for their robustness. However, topological conversion schemes require strict compatibility conditions that inevitably increase element count. State-of-the-art 2-refinement octree methods employ weakly-balanced and generalized pairing conditions to yield low element counts, but suffer from critical limitations: primal cell information is lost after dualization, and resulting dual cells often exhibit non-planar quad faces. Alternatively, 3-refinement 27-tree methods directly generate conforming hex meshes through template-based replacement, producing higher-quality elements with planar faces, but previous techniques impose far stricter conditions, severely over-refining grids by factors of ten to one hundred. This article introduces a novel 3-refinement approach using a moderately-balanced condition, slightly stronger than weakly-balanced but substantially more relaxed than prior 3-refinement requirements. The key insight is that recursively applying local refinements can isolate and reduce complex configurations to simpler cases covered by a fundamental template set. Two open-sourced variants are provided: one optimized for speed, and another trading some computational cost for marginally reduced element counts. Compared to previous 3-refinement methods, they significantly reduce final hex element counts while preserving min SJ values and guaranteeing convex polyhedral cells; relative to 2-refinement state-of-the-art, they also achieve a lower Hausdorff ratio using slightly fewer elements.

Liang Jin, Shixuan Gu, Donglai Wei et al. · harvard

Automatic rib labeling and anatomical centerline extraction are common prerequisites for various clinical applications. Prior studies either use in-house datasets that are inaccessible to communities, or focus on rib segmentation that neglects the clinical significance of rib labeling. To address these issues, we extend our prior dataset (RibSeg) on the binary rib segmentation task to a comprehensive benchmark, named RibSeg v2, with 660 CT scans (15,466 individual ribs in total) and annotations manually inspected by experts for rib labeling and anatomical centerline extraction. Based on the RibSeg v2, we develop a pipeline including deep learning-based methods for rib labeling, and a skeletonization-based method for centerline extraction. To improve computational efficiency, we propose a sparse point cloud representation of CT scans and compare it with standard dense voxel grids. Moreover, we design and analyze evaluation metrics to address the key challenges of each task. Our dataset, code, and model are available online to facilitate open research at https://github.com/M3DV/RibSeg

Hua Tong, Kuanren Qian, Eni Halilaj et al.

High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual processing and has long been considered the most challenging and time-consuming bottleneck of the entire modeling and analysis process. In this paper, we present a novel computational framework named ``SRL-assisted AFM" for meshing planar geometries by combining the advancing front method with neural networks that select reference vertices and update the front boundary using ``policy networks." These deep neural networks are trained using a unique pipeline that combines supervised learning with reinforcement learning to iteratively improve mesh quality. First, we generate different initial boundaries by randomly sampling points in a square domain and connecting them sequentially. These boundaries are used for obtaining input meshes and extracting training datasets in the supervised learning module. We then iteratively improve the reinforcement learning model performance with reward functions designed for special requirements, such as improving the mesh quality and controlling the number and distribution of extraordinary points. Our proposed supervised learning neural networks achieve an accuracy higher than 98% on predicting commercial software. The final reinforcement learning neural networks automatically generate high-quality quadrilateral meshes for complex planar domains with sharp features and boundary layers.

Yuxuan Yu, Jiashuo Liu, Hua Tong et al.

Polycube structures provide parametric domains for all-hexahedral (all-hex) mesh generation and analysis-suitable volumetric spline construction in isogeometric analysis (IGA). Recent learning-based polycube pipelines have improved automation, yet several challenges remain when handling complex CAD geometries. These challenges include the limited diversity of primitive geometries, restricted grid configurations, and the increasing cost of genus-guided context search during inference as both the primitive set and the grid size grow. In this paper, we present {Scalable DDPM-Polycube}, an extended diffusion-based polycube construction method that addresses these limitations. First, we expand the primitive set from two primitive geometries to three by introducing a blind-hole cube primitive, thereby improving the representation of local hole-like features that do not change the global genus. Second, we extend the grid configuration from the previous $2\times 1$ setting to an enlarged three-dimensional grid configuration, which increases representational capacity and reduces mapping distortion for complex geometries. Third, we develop a genus-guided context generation strategy together with a hierarchical verification procedure, enabling robust context generation in both user-guided and automated modes. Once a valid polycube structure is generated, it is used for parametric mapping, all-hex control mesh generation, and volumetric spline construction. Experimental results demonstrate that scalable DDPM-Polycube improves the generality, scalability, and automation of diffusion-based polycube generation, and supports hex mesh generation and volumetric spline construction for IGA applications on complex geometries.

Vedant Puri, Aditya Joglekar, Kevin Ferguson et al.

The quadratic complexity of self-attention limits its applicability and scalability on large unstructured meshes. We introduce Fast Low-rank Attention Routing Engine (FLARE), a linear complexity self-attention mechanism that routes attention through fixed-length latent sequences. Each attention head performs global communication among $N$ tokens by projecting the input sequence onto a fixed length latent sequence of $M \ll N$ tokens using learnable query tokens. By routing attention through a bottleneck sequence, FLARE learns a low-rank form of attention that can be applied at $O(NM)$ cost. FLARE not only scales to unprecedented problem sizes, but also delivers superior accuracy compared to state-of-the-art neural PDE surrogates across diverse benchmarks. We also release a new additive manufacturing dataset to spur further research. Our code is available at https://github.com/vpuri3/FLARE.py.

Yuxuan Yu, Yuzhuo Fang, Hua Tong et al.

In this paper, we present a novel algorithm that integrates deep learning with the polycube method (DL-Polycube) to generate high-quality hexahedral (hex) meshes, which are then used to construct volumetric splines for isogeometric analysis. Our DL-Polycube algorithm begins by establishing a connection between surface triangular meshes and polycube structures. We employ deep neural network to classify surface triangular meshes into their corresponding polycube structures. Following this, we combine the acquired polycube structural information with unsupervised learning to perform surface segmentation of triangular meshes. This step addresses the issue of segmentation not corresponding to a polycube while reducing manual intervention. Quality hex meshes are then generated from the polycube structures, with employing octree subdivision, parametric mapping and quality improvement techniques. The incorporation of deep learning for creating polycube structures, combined with unsupervised learning for segmentation of surface triangular meshes, substantially accelerates hex mesh generation. Finally, truncated hierarchical B-splines are constructed on the generated hex meshes. We extract trivariate Bézier elements from these splines and apply them directly in isogeometric analysis. We offer several examples to demonstrate the robustness of our DL-Polycube algorithm.

Steven Owen, Nathan Brown, Nikos Chrisochoides et al.

Artificial intelligence is beginning to reduce the manual effort in the CAD-to-mesh pipeline. Written for meshing and geometry practitioners with limited AI background, this survey organizes recent work by workflow step. We cover part classification and segmentation, mesh quality prediction, and defeaturing. We review AI guidance for unstructured meshing, block-structured meshing in 2D and 3D, and volumetric parameterization, including reconstruction from implicit or sampled geometry. We also discuss parallel mesh generation and scripting automation via reinforcement learning and large language models. Across these topics, AI complements established geometry and meshing algorithms rather than replacing them. We conclude with practical lessons and open challenges in data, benchmarks, and trustworthy integration.

Tsung Yeh Hsieh, Yongjie Jessica Zhang

Neurons exhibit intricate geometries within their neurite networks, which play a crucial role in processes such as signaling and nutrient transport. Accurate simulation of material transport in the networks is essential for understanding these biological phenomena but poses significant computational challenges because of the complex tree-like structures involved. Traditional approaches are time-intensive and resource-demanding, yet the inherent properties of neuron trees, which consists primarily of pipes with steady-state parabolic velocity profiles and bifurcations, provide opportunities for computational optimization. To address these challenges, we propose a Graph-Autoencoder-based Latent Dynamics Surrogate (GALDS) model, which is specifically designed to streamline the simulation of material transport in neural trees. GALDS employs a graph autoencoder to encode latent representations of the network's geometry, velocity fields, and concentration profiles. These latent space representations are then assembled into a global graph, which is subsequently used to predict system dynamics in the latent space via a trained graph latent space system dynamic model, inspired by the Neural Ordinary Differential Equations (Neural ODEs) concept. The integration of an autoencoder allows for the use of smaller graph neural network models with reduced training data requirements. Furthermore, the Neural ODE component effectively mitigates the issue of error accumulation commonly encountered in recurrent neural networks. The effectiveness of the GALDS model is demonstrated through results on eight unseen geometries and four abnormal transport examples, where our approach achieves mean relative error of 3% with maximum relative error <8% and demonstrates a 10-fold speed improvement compared to previous surrogate model approaches.

Kuanren Qian, Genesis Omana Suarez, Toshihiko Nambara et al.

Neurodevelopmental disorders (NDDs) cover a variety of conditions, including autism spectrum disorder, attention-deficit/hyperactivity disorder, and epilepsy, which impair the central and peripheral nervous systems. Their high comorbidity and complex etiologies present significant challenges for accurate diagnosis and effective treatments. Conventional clinical and experimental studies are time-intensive, burdening research progress considerably. This paper introduces a high-throughput digital twin framework for modeling neurite deteriorations associated with NDDs, integrating synthetic data generation, experimental images, and machine learning (ML) models. The synthetic data generator utilizes an isogeometric analysis (IGA)-based phase field model to capture diverse neurite deterioration patterns such as neurite retraction, atrophy, and fragmentation while mitigating the limitations of scarce experimental data. The ML model utilizes MetaFormer-based gated spatiotemporal attention architecture with deep temporal layers and provides fast predictions. The framework effectively captures long-range temporal dependencies and intricate morphological transformations with average errors of 1.9641% and 6.0339% for synthetic and experimental neurite deterioration, respectively. Seamlessly integrating simulations, experiments, and ML, the digital twin framework can guide researchers to make informed experimental decisions by predicting potential experimental outcomes, significantly reducing costs and saving valuable time. It can also advance our understanding of neurite deterioration and provide a scalable solution for exploring complex neurological mechanisms, contributing to the development of targeted treatments.

Leslie Gu, Jason Ken Adhinarta, Mikhail Bessmeltsev et al. · harvard

Accurately segmenting 3D curvilinear structures in medical imaging remains challenging due to their complex geometry and the scarcity of diverse, large-scale datasets for algorithm development and evaluation. In this paper, we use dendritic spine segmentation as a case study and address these challenges by introducing a novel Frenet--Serret Frame-based Decomposition, which decomposes 3D curvilinear structures into a globally \( C^2 \) continuous curve that captures the overall shape, and a cylindrical primitive that encodes local geometric properties. This approach leverages Frenet--Serret Frames and arc length parameterization to preserve essential geometric features while reducing representational complexity, facilitating data-efficient learning, improved segmentation accuracy, and generalization on 3D curvilinear structures. To rigorously evaluate our method, we introduce two datasets: CurviSeg, a synthetic dataset for 3D curvilinear structure segmentation that validates our method's key properties, and DenSpineEM, a benchmark for dendritic spine segmentation, which comprises 4,476 manually annotated spines from 70 dendrites across three public electron microscopy datasets, covering multiple brain regions and species. Our experiments on DenSpineEM demonstrate exceptional cross-region and cross-species generalization: models trained on the mouse somatosensory cortex subset achieve 91.9\% Dice, maintaining strong performance in zero-shot segmentation on both mouse visual cortex (94.1\% Dice) and human frontal lobe (81.8\% Dice) subsets. Moreover, we test the generalizability of our method on the IntrA dataset, where it achieves 77.08\% Dice (5.29\% higher than prior arts) on intracranial aneurysm segmentation. These findings demonstrate the potential of our approach for accurately analyzing complex curvilinear structures across diverse medical imaging fields.

Humphrey Yang, Kuanren Qian, Haolin Liu et al.

Morphing materials allow us to create new modalities of interaction and fabrication by leveraging dynamic behaviors of materials. Yet, despite the ongoing rapid growth of computational tools within this realm, current developments are bottlenecked by the lack of an effective simulation method. As a result, existing design tools must trade-off between speed and accuracy to support a real-time interactive design scenario. In response, we introduce SimuLearn, a data-driven method that combines finite element analysis and machine learning to create real-time (0.61 seconds) and truthful (97% accuracy) morphing material simulators. We use mesh-like 4D printed structures to contextualize this method and prototype design tools to exemplify the design workflows and spaces enabled by a fast and accurate simulation method. Situating this work among existing literature, we believe SimuLearn is a timely addition to the HCI CAD toolbox that can enable the proliferation of morphing materials.