arXiv subjects

Yongjie Jessica Zhang

Publications and source records attributed to Yongjie Jessica Zhang.

At least 19 recordsLinked to original sources

arXiv2026

JAXIGA - A software framework for GPU-enabled and differentiable isogeometric analysis

In this paper, we present JAXIGA, an open-source library for isogeometric analysis based on JAX. The library separates the construction of the mesh from the computations which are traced for compilation and differentiation. This allows geometry evaluation, assembly and the supported solvers to be combined in a just-in-time compiled program, for which first-order reverse-mode derivatives can be computed. We consider three numerical methods obtained from a single pointwise energy density. The Galerkin and energy-minimization methods use the same discrete potential and have the same stationary points, while collocation enforces the corresponding strong form. The sensitivities of a converged solution are obtained by solving one adjoint problem, and their accuracy depends on the tolerances of both the primal and adjoint problems. We also describe hierarchical extraction for local refinement of the variational methods and the use of smooth spline spaces for fourth-order problems. The numerical results are compared with analytical solutions and independent FEniCSx and JAX-FEM computations. For the reported GPU benchmark with 36,448 unknowns, assembly is twenty-four times faster than on the host CPU. When the conjugate-gradient solver is also run on the GPU, the total solution time is reduced from 31.8 to 1.38 seconds, and the result agrees with the direct solution to $5\times10^{-11}$. These results show that the choice of solver and the reuse of compilation are important for obtaining an overall reduction in computational cost.

math.NA↗

arXiv2026

FLARE++: Low-rank attention with dynamic attention routing

Full self-attention is a strong token mixer for PDE surrogates on irregular domains, but its quadratic cost limits its use on large problems. Latent-space attention methods such as PerceiverIO, Transolver, and FLARE (Fast Low-rank Attention Routing Engine) avoid that cost by routing attention among $N$ tokens through $M\ll N$ learned latents. They compress by dot-product matching of the input tokens against $M$ learned query tokens or projection weights: once trained, the same learned templates serve every input. We remove this restriction with FLARE++, a low-rank attention architecture with input-conditioned routing queries. FLARE++ uses FLARE's own encoder to map the $N$ input tokens to $M$ query tokens, which correct the learned queries. The adapted queries then determine how that same input is compressed and redistributed. This preserves FLARE's explicit low-rank factorization and linear $\mathcal O(NM)$ complexity, and expresses the complete routing operation with standard scaled dot-product attention (SDPA) calls alone. We also provide a multi-GPU context-parallel implementation that shards input tokens across devices without ever gathering the full token sequence on one of them. FLARE++ reduces FLARE's error by $25\%$ on average across five standard PDE benchmarks, achieving the lowest errors among the efficient models compared. The gains persist on industrial-scale DrivAerML aerodynamics and on Long Range Arena, where average accuracy rises by $3.5\%$ over fixed-query FLARE. Code is available at https://github.com/vpuri3/FLARE.py.

cs.LG↗

arXiv2026

Planar-faced and high-Jacobian two-refinement hexahedral templates

Automatically generating high-quality conforming hexahedral (hex) meshes from general input boundaries remains a challenging problem, despite the numerical advantages hex elements offer in simulation. Grid-based adaptive refinement, followed by hanging-node removal, is the most robust fully automatic choice. Among two-refinement methods, primal templates have better mesh quality than dual templates but depend on a strong balancing condition that over-refines the grid; neither family guarantees planar quadrilateral (quad) faces. This paper generalizes recent primal three-refinement templates to a two-refinement scheme under a moderate balancing condition, a relaxation of the strong one. 32 special and five fundamental patterns resolve all 144 symmetry-reduced configurations, followed by either a fast greedy algorithm or an integer linear programming (ILP) algorithm that trades extra runtime for a further reduction in element count. The scheme is the first two-refinement method in which all hexes have planar faces, and its meshes feed directly into a recent quality-guaranteed hex mesh reconstruction algorithm. At comparable element counts, it attains a similar Hausdorff ratio (HR) and a higher minimum scaled Jacobian (min SJ) than its three-refinement counterpart.

cs.GR↗

arXiv2026

MGRD: Compact morphology-gated residual diffusion for variance-aware cross-domain neurite forecasting

Tracking neurite morphology over time helps characterize structural changes during neuronal development and deterioration, but long-term time-lapse imaging is resource-intensive and difficult to scale. Forecasting future morphology could reduce this burden. Existing neurite digital-twin models such as gated spatiotemporal attention (gSTA) produce a single deterministic forecast without representing variability among plausible futures. We introduce Morphology-Gated Residual Diffusion (MGRD), a compact stochastic surrogate that jointly forecasts twenty future neurite-morphology frames from ten observed frames while conditioning on morphology features derived from the latest observation. On controlled phase-field trajectories, MGRD reduces trajectory-wise mean MAE by 9.7% relative to a matched control while updating 4.46 times fewer parameters. On human iPSC-derived neuron microscopy, MGRD improves all four reported metrics over gSTA, including a 39.6% reduction in trajectory-wise mean MAE and a 45.3% increase in skeleton F1. Without mouse-domain retraining or fine-tuning, MGRD also improves MAE and skeleton F1 on mouse cortical-neurosphere microscopy across 10-40-min sampling intervals and forecast horizons beyond 13 hours. Repeated sampling provides a case-level variance score for ranking forecast difficulty. Retaining approximately 60% of the lowest-variance cases reduces mean MAE by 17.6% on iPSC microscopy and 16.8% on simulation data. MGRD uses 1.01% of gSTA's parameters, requires less than one tenth of its training-update time, and generates a 50-step DDIM trajectory 7.9% faster when morphology features are cached. These results establish MGRD as a compact stochastic surrogate for neurite-morphology forecasting and case prioritization across simulation and microscopy datasets.

cs.LG↗

arXiv2026

MCHex: Marching Cubes Based Adaptive Hexahedral Mesh Generation with Guaranteed Positive Jacobian

Grid-based methods are the most robust approach for automatic hexahedral (hex) meshing, but they struggle to achieve high boundary fidelity and element quality. Conventional pipelines remove outside elements. This yields axis-aligned surfaces that converge to the input geometry at first order. The subsequent padding and projection steps are heuristic, offering no guarantees on final boundary fidelity or mesh quality. This paper introduces MCHex, a fundamental reformulation of boundary and mesh quality handling in grid-based hex meshing. MCHex directly applies Marching Cubes (MC) inside each grid cell, ensuring that the mesh boundary is an MC surface. The key insight is that by constraining cut-cell configurations to a 3-regular polyhedron, a midpoint subdivision of these configurations produces an all-hex mesh with a guaranteed positive Jacobian for every element. MCHex provides three advantages: (1) a theoretical guarantee of positive Jacobian for all hex elements; (2) boundary convergence that matches the approximation rate of MC, together with a non-heuristic algorithm that has well-bounded time complexity and achieves the fastest wall-clock time among all existing methods; and (3) generation of manifold surfaces for arbitrary geometries and a natural padded layer. Extensive evaluation on a benchmark of 202 geometries compares MCHex against several previous state-of-the-art hex meshing methods under a slightly smaller element budget, demonstrating that MCHex consistently produces positive Jacobian meshes with similar boundary fidelity while running significantly faster. MCHex can integrate seamlessly with post-processing steps such as mesh smoothing, mesh simplification, and is suitable for simulation.

cs.CG↗

arXiv2026

Element-Saving Hexahedral 3-Refinement Templates

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.

cs.CG↗

arXiv2026

Scalable DDPM-Polycube: An Extended Diffusion-Based Method for Hexahedral Mesh and Volumetric Spline Construction

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.

cs.CE↗

arXiv2026

A Survey of AI Methods for Geometry Preparation and Mesh Generation in Engineering Simulation

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.

cs.CE↗

arXiv2026

FLARE: Fast Low-rank Attention Routing Engine

The quadratic complexity of self-attention limits the scalability of transformers on long sequences. We introduce Fast Low-rank Attention Routing Engine (FLARE), a token-mixing operator that realizes low-rank attention by routing information through a small set of latent tokens. Each layer induces an input-input token mixing matrix of rank at most $M$ via a minimal encode-decode factorization implemented using only two standard scaled dot-product attention (SDPA) calls. Because the dominant ${O}(NM)$ computation is expressed purely in terms of standard SDPA, FLARE is compatible with fused attention kernels and avoids materializing $M\times N$ projection matrices. FLARE further assigns disjoint latent slices to each attention head, yielding a mixture of head-specific low-rank pathways. Empirically, FLARE scales to one-million-point unstructured meshes on a single GPU, achieves state-of-the-art accuracy on PDE surrogate benchmarks, and outperforms general-purpose efficient-attention methods on the Long Range Arena suite. We additionally release a large-scale additive manufacturing benchmark dataset. Our code is available at https://github.com/vpuri3/FLARE.py.

cs.LG↗

arXiv2025

GALDS: A Graph-Autoencoder-based Latent Dynamics Surrogate model to predict neurite material transport

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.

cs.LG↗

arXiv2025

Frenet-Serret Frame-based Decomposition for Part Segmentation of 3D Curvilinear Structures

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.

cs.CV↗

arXiv2025

3D neuron growth and neurodevelopmental disorder modeling based on truncated hierarchical B-splines with multi-level local refinements

3D neuron growth and neurodevelopmental disorders (NDDs) deterioration exhibit complex morphological transformations as neurites differentiate into axons and dendrites, forming intricate networks driven by tubulin concentrations and neurotrophin signals. Conventional 2D models fall short of capturing such morphological complexity, prompting the need and development of advanced 3D computational approaches. In this paper, we present a complex 3D neuron growth model based on isogeometric analysis (IGA) and the phase field method, utilizing locally refined truncated hierarchical B-splines (THB-splines). IGA offers isoparametric representation and higher-order continuity, which are essential for simulating the smooth, evolving interfaces of phase field neurites. In contrast, the phase field method can automatically handle diffuse interfaces and complex topological changes without explicit boundary tracking. This IGA-based phase field method enables accurate and efficient simulation of neurite extensions, branching, and retraction in a fully 3D setting. The THB-spline implementation supports multi-level local refinement, focusing computational resources on regions of active growth, while dynamic domain expansion adapts the simulation domain to extend with growing neurites. KD-tree-based interpolation ensures that phase field variables are accurately transferred onto newly refined meshes. NDDs associated neurite deterioration is simulated by modulating the driving force term within the phase field model to induce interface retraction. This comprehensive 3D framework enhances the accuracy of neurite morphology simulations, advancing the study of complex neuron development, network formation and NDDs.

physics.med-ph↗

arXiv2025

DDPM-Polycube: A Denoising Diffusion Probabilistic Model for Polycube-Based Hexahedral Mesh Generation and Volumetric Spline Construction

In this paper, we propose DDPM-Polycube, a generative polycube creation approach based on denoising diffusion probabilistic models (DDPM) for generating high-quality hexahedral (hex) meshes and constructing volumetric splines. Unlike DL-Polycube methods that rely on predefined polycube structure templates, DDPM-Polycube models the deformation from input geometry to its corresponding polycube structures as a denoising task. By learning the deformation characteristics of simple geometric primitives (a cube and a cube with a hole), the DDPM-Polycube model progressively reconstructs polycube structures from input geometry by removing non-standard Gaussian noise. Once valid polycube structures are generated, they are used for surface segmentation and parametric mapping to generate high-quality hex meshes. Truncated hierarchical B-splines are then applied to construct volumetric splines that satisfy the requirements of isogeometric analysis (IGA). Experimental results demonstrate that DDPM-Polycube model can directly generate polycube structures from input geometries, even when the topology of these geometries falls outside its trained range. This provides greater generalization and adaptability for diverse engineering geometries. Overall, this research shows the potential of diffusion models in advancing mesh generation and IGA applications.

cs.GR↗

arXiv2024

Fast and Robust Hexahedral Mesh Optimization via Augmented Lagrangian, L-BFGS, and Line Search

We present a new software package, ``HexOpt,'' for improving the quality of all-hexahedral (all-hex) meshes by maximizing the minimum mixed scaled Jacobian-Jacobian energy functional, and projecting the surface points of the all-hex meshes onto the input triangular mesh. The proposed HexOpt method takes as input a surface triangular mesh and a volumetric all-hex mesh. A constrained optimization problem is formulated to improve mesh quality using a novel function that combines Jacobian and scaled Jacobian metrics which are rectified and scaled to quadratic measures, while preserving the surface geometry. This optimization problem is solved using the augmented Lagrangian (AL) method, where the Lagrangian terms enforce the constraint that surface points must remain on the triangular mesh. Specifically, corner points stay exactly at the corner, edge points are confined to the edges, and face points are free to move across the surface. To take the advantage of the Quasi-Newton method while tackling the high-dimensional variable problem, the Limited-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm is employed. The step size for each iteration is determined by the Armijo line search. Coupled with smart Laplacian smoothing, HexOpt has demonstrated robustness and efficiency, successfully applying to 3D models and hex meshes generated by different methods without requiring any manual intervention or parameter adjustment.

cs.CG↗

arXiv2024

High-throughput digital twin framework for predicting neurite deterioration using MetaFormer attention

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.

q-bio.NC↗

arXiv2024

DL-Polycube: Deep learning enhanced polycube method for high-quality hexahedral mesh generation and volumetric spline construction

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.

cs.CG↗

arXiv2024

Nonintrusive projection-based reduced order modeling using stable learned differential operators

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov-Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through three numerical experiments: 1-D advection equation, 1-D Burgers equation and 2-D advection equation. The results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.

physics.comp-ph↗

arXiv2024

SNF-ROM: Projection-based nonlinear reduced order modeling with smooth neural fields

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While commonly used, linear subspace reduced-order models (ROMs) are often suboptimal for problems with a slow decay of Kolmogorov $n$-width, such as advection-dominated fluid flows at high Reynolds numbers. There has been a growing interest in nonlinear ROMs that use state-of-the-art representation learning techniques to accurately capture such phenomena with fewer degrees of freedom. We propose smooth neural field ROM (SNF-ROM), a nonlinear reduced modeling framework that combines grid-free reduced representations with Galerkin projection. The SNF-ROM architecture constrains the learned ROM trajectories to a smoothly varying path, which proves beneficial in the dynamics evaluation when the reduced manifold is traversed in accordance with the governing PDEs. Furthermore, we devise robust regularization schemes to ensure the learned neural fields are smooth and differentiable. This allows us to compute physics-based dynamics of the reduced system nonintrusively with automatic differentiation and evolve the reduced system with classical time-integrators. SNF-ROM leads to fast offline training as well as enhanced accuracy and stability during the online dynamics evaluation. Numerical experiments reveal that SNF-ROM is able to accelerate the full-order computation by up to $199\times$. We demonstrate the efficacy of SNF-ROM on a range of advection-dominated linear and nonlinear PDE problems where we consistently outperform state-of-the-art ROMs.

physics.flu-dyn↗