arXiv subjects

Yongjie Jessica Zhang

Publications and source records attributed to Yongjie Jessica Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Neurodevelopmental disorders modeling using isogeometric analysis, dynamic domain expansion and local refinement

Neurodevelopmental disorders (NDDs) have arisen as one of the most prevailing chronic diseases within the US. Often associated with severe adverse impacts on the formation of vital central and peripheral nervous systems during the neurodevelopmental process, NDDs are comprised of a broad spectrum of disorders, such as autism spectrum disorder, attention deficit hyperactivity disorder, and epilepsy, characterized by progressive and pervasive detriments to cognitive, speech, memory, motor, and other neurological functions in patients. However, the heterogeneous nature of NDDs poses a significant roadblock to identifying the exact pathogenesis, impeding accurate diagnosis and the development of targeted treatment planning. A computational NDDs model holds immense potential in enhancing our understanding of the multifaceted factors involved and could assist in identifying the root causes to expedite treatment development. To tackle this challenge, we introduce optimal neurotrophin concentration to the driving force and degradation of neurotrophin to the synaptogenesis process of a 2D phase field neuron growth model using isogeometric analysis to simulate neurite retraction and atrophy. The optimal neurotrophin concentration effectively captures the inverse relationship between neurotrophin levels and neurite survival, while its degradation regulates concentration levels. Leveraging dynamic domain expansion, the model efficiently expands the domain based on outgrowth patterns to minimize degrees of freedom. Based on truncated T-splines, our model simulates the evolving process of complex neurite structures by applying local refinement adaptively to the cell/neurite boundary. Furthermore, a thorough parameter investigation is conducted with detailed comparisons against neuron cell cultures in experiments, enhancing our fundamental understanding of the mechanisms underlying NDDs.

q-bio.NC↗

arXiv2024

Data-driven identification of stable differential operators using constrained regression

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics forecasting problems. In this article, we propose a novel methodology for learning sparse differential operators that are theoretically linearly stable by solving a constrained regression problem. These underlying constraints are obtained following linear stability for dynamical systems. We further extend this approach for learning nonlinear differential operators by determining linear stability constraints for linearized equations around an equilibrium point. The applicability of the proposed method is demonstrated for both linear and nonlinear partial differential equations such as 1-D scalar advection-diffusion equation, 1-D Burgers equation and 2-D advection equation. The results indicated that solutions to constrained regression problems with linear stability constraints provide accurate and linearly stable sparse differential operators.

math.NA↗

arXiv2024

Projection-based reduced order modeling and data-driven artificial viscosity closures for incompressible fluid flows

Projection-based reduced order models rely on offline-online model decomposition, where the data-based energetic spatial basis is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the inexpensive online stage. The online stage requires a solution method for the dynamic evolution of the coupled system of pressure and velocity states for incompressible fluid flows. The first contribution of this article is to demonstrate the applicability of the incremental pressure correction scheme for the dynamic evolution of pressure and velocity states. The evolution of a large number of these reduced states in the online stage can be expensive. In contrast, the accuracy significantly decreases if only a few reduced states are considered while not accounting for the interactions between unresolved and resolved states. The second contribution of this article is to compare three closure model forms based on global, modal and tensor artificial viscosity approximation to account for these interactions. The unknown model parameters are determined using two calibration techniques: least squares minimization of error in energy approximation and closure term approximation. This article demonstrates that an appropriate selection of solution methods and data-driven artificial viscosity closure models is essential for consistently accurate dynamics forecasting of incompressible fluid flows.

physics.flu-dyn↗

arXiv2024

HybridOctree_Hex: Hybrid Octree-Based Adaptive All-Hexahedral Mesh Generation with Jacobian Control

We present a new software package, "HybridOctree_Hex," for adaptive all-hexahedral mesh generation based on hybrid octree and quality improvement with Jacobian control. The proposed HybridOctree_Hex begins by detecting curvatures and narrow regions of the input boundary to identify key surface features and initialize an octree structure. Subsequently, a strongly balanced octree is constructed using the balancing and pairing rules. Inspired by our earlier preliminary hybrid octree-based work, templates are designed to guarantee an all-hexahedral dual mesh generation directly from the strongly balanced octree. With these pre-defined templates, the sophisticated hybrid octree construction step is skipped to achieve an efficient implementation. After that, elements outside and around the boundary are removed to create a core mesh. The boundary points of the core mesh are connected to their corresponding closest points on the surface to fill the buffer zone and build the final mesh. Coupled with smart Laplacian smoothing, HybridOctree_Hex takes advantage of a delicate optimization-based quality improvement method considering geometric fitting, Jacobian and scaled Jacobian, to achieve a minimum scaled Jacobian that is higher than $0.5$. We empirically verify the robustness and efficiency of our method by running the HybridOctree_Hex software on dozens of complex 3D models without any manual intervention or parameter adjustment. We provide the HybridOctree_Hex source code, along with comprehensive results encompassing the input and output files and statistical data in the following repository: https://github.com/CMU-CBML/HybridOctree_Hex.

cs.CG↗

arXiv2023

$pκ$-Curves: Interpolatory curves with curvature approximating a parabola

This paper introduces a novel class of fair and interpolatory curves called $pκ$-curves. These curves are comprised of smoothly stitched Bézier curve segments, where the curvature distribution of each segment is made to closely resemble a parabola, resulting in an aesthetically pleasing shape. Moreover, each segment passes through an interpolated point at a parameter where the parabola has an extremum, encouraging the alignment of interpolated points with curvature extrema. To achieve these properties, we tailor an energy function that guides the optimization process to obtain the desired curve characteristics. Additionally, we develop an efficient algorithm and an initialization method, enabling interactive modeling of the $pκ$-curves without the need for global optimization. We provide various examples and comparisons with existing state-of-the-art methods to demonstrate the curve modeling capabilities and visually pleasing appearance of $pκ$-curves.

cs.CG↗

arXiv2023

RibSeg v2: A Large-scale Benchmark for Rib Labeling and Anatomical Centerline Extraction

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

eess.IV↗

arXiv2023

SRL-Assisted AFM: Generating Planar Unstructured Quadrilateral Meshes with Supervised and Reinforcement Learning-Assisted Advancing Front Method

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.

math.NA↗

arXiv2023

Biomimetic IGA neuron growth modeling with neurite morphometric features and CNN-based prediction

Neuron growth is a complex, multi-stage process that develops sophisticated morphologies and interwoven neurite networks. Recent advances have enabled us to examine the effects of neuron growth factors and seek causes for neurodegenerative diseases, such as Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis. A computational tool that studies neuron growth could shed crucial insights into the effects of various factors and help find a neurodegeneration cure. However, there lacks a computational tool to accurately and realistically simulate neuron growth within reasonable time frames. Bio-phenomenon models ignore potential factors and cannot generate realistic results, and bio-physics models require computationally expensive high-order governing equations. This paper incorporates experimental neurite features into a phase field method-based neuron growth model using an isogeometric analysis collocation (IGA-C) approach. Based on a semi-automated quantitative analysis of neurite morphology, we obtain relative turning angle, average tortuosity, neurite endpoints, average segment length, and the total length of neurites. We use the total neurite length to determine the evolving days in vitro (DIV) and select corresponding neurite features to drive and constrain neuron growth. This approach archives biomimetic neuron growth patterns with automatic growth stage transitions by incorporating corresponding DIV neurite morphometric data based on the total neurite length of the evolving neurite morphology. Furthermore, we built a convolutional neural network (CNN) to significantly reduce computational costs for predicting neurite growth. With a customized convolutional autoencoder as the backbone, our CNN model can predict neurite patterns with a high prediction accuracy, 97.77%, while taking 7 orders of magnitude less computational times than our IGA-C solver.

math.NA↗

arXiv2023

Kirchhoff-Love shell representation and analysis using triangle configuration B-splines

This paper presents the application of triangle configuration B-splines (TCB-splines) for representing and analyzing the Kirchhoff-Love shell in the context of isogeometric analysis (IGA). The Kirchhoff-Love shell formulation requires global $C^1$-continuous basis functions. The nonuniform rational B-spline (NURBS)-based IGA has been extensively used for developing Kirchhoff-Love shell elements. However, shells with complex geometries inevitably need multiple patches and trimming techniques, where stitching patches with high continuity is a challenge. On the other hand, due to their unstructured nature, TCB-splines can accommodate general polygonal domains, have local refinement, and are flexible to model complex geometries with $C^1$ continuity, which naturally fit into the Kirchhoff-Love shell formulation with complex geometries. Therefore, we propose to use TCB-splines as basis functions for geometric representation and solution approximation. We apply our method to both linear and nonlinear benchmark shell problems, where the accuracy and robustness are validated. The applicability of the proposed approach to shell analysis is further exemplified by performing geometrically nonlinear Kirchhoff-Love shell simulations of a pipe junction and a front bumper represented by a single patch of TCB-splines.

cs.CE↗

arXiv2021

Modeling material transport regulation and traffic jam in neurons using PDE-constrained optimization

The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of transport. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in complex geometries of neurons. The transport is controlled to avoid traffic jam of materials by minimizing a pre-defined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using isogeometric analysis (IGA). Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neuron.

physics.bio-ph↗

arXiv2021

HexDom: Polycube-Based Hexahedral-Dominant Mesh Generation

In this paper, we extend our earlier polycube-based all-hexahedral mesh generation method to hexahedral-dominant mesh generation, and present the HexDom software package. Given the boundary representation of a solid model, HexDom creates a hex-dominant mesh by using a semi-automated polycube-based mesh generation method. The resulting hexahedral dominant mesh includes hexahedra, tetrahedra, and triangular prisms. By adding non-hexahedral elements, we are able to generate better quality hexahedral elements than in all-hexahedral meshes. We explain the underlying algorithms in four modules including segmentation, polycube construction, hex-dominant mesh generation and quality improvement, and use a rockerarm model to explain how to run the software. We also apply our software to a number of other complex models to test their robustness. The software package and all tested models are availabe in github (https://github.com/CMU-CBML/HexDom).

cs.GR↗

arXiv2021

Deep learning of material transport in complex neurite networks

Neurons exhibit complex geometry in their branched networks of neurites which is essential to the function of individual neuron but also brings challenges to transport a wide variety of essential materials throughout their neurite networks for their survival and function. While numerical methods like isogeometric analysis (IGA) have been used for modeling the material transport process via solving partial differential equations (PDEs), they require long computation time and huge computation resources to ensure accurate geometry representation and solution, thus limit their biomedical application. Here we present a graph neural network (GNN)-based deep learning model to learn the IGA-based material transport simulation and provide fast material concentration prediction within neurite networks of any topology. Given input boundary conditions and geometry configurations, the well-trained model can predict the dynamical concentration change during the transport process with an average error less than 10% and 120~330 times faster compared to IGA simulations. The effectiveness of the proposed model is demonstrated within several complex neurite networks.

cs.CE↗

arXiv2021

Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines to allow multiple extraordinary points within the same face. This generalization drastically increases the flexibility to build geometries using AST-splines; e.g., much coarser meshes can be generated to represent a certain geometry. The AST-spline spaces detailed in this work have $C^1$ inter-element continuity near extraordinary points and $C^2$ inter-element continuity elsewhere. We mathematically show that AST-splines with multiple extraordinary points per face are linearly independent and their polynomial basis functions form a non-negative partition of unity. We numerically show that AST-splines with multiple extraordinary points per face lead to optimal convergence rates for second- and fourth-order linear elliptic problems. To illustrate a possible isogeometric framework that is already available, we design the B-pillar and the side outer panel of a car using T-splines with the commercial software Autodesk Fusion360, import the control nets into our in-house code to build AST-splines, and import the Bézier extraction information into the commercial software LS-DYNA to solve eigenvalue problems. The results are compared with conventional finite elements. Good agreement is found, but conventional finite elements require significantly more degrees of freedom to reach a converged solution than AST-splines.

math.NA↗

arXiv2020

HexGen and Hex2Spline: Polycube-based Hexahedral Mesh Generation and Spline Modeling for Isogeometric Analysis Applications in LS-DYNA

In this paper, we present two software packages, HexGen and Hex2Spline, that seamlessly integrate geometry design with isogeometric analysis (IGA) in LS-DYNA. Given a boundary representation of a solid model, HexGen creates a hexahedral mesh by utilizing a semi-automatic polycube-based mesh generation method. Hex2Spline takes the output hexahedral mesh from HexGen as the input control mesh and constructs volumetric truncated hierarchical splines. Through Bézier extraction, Hex2Spline transfers spline information to LS-DYNA and performs IGA therein. We explain the underlying algorithms in each software package and use a rod model to explain how to run the software. We also apply our software to several other complex models to test its robustness. Our goal is to provide a robust volumetric modeling tool and thus expand the boundary of IGA to volume-based industrial applications.

cs.CG↗

arXiv2020

Material characterization and precise finite element analysis of fiber reinforced thermoplastic composites for 4D printing

Four-dimensional (4D) printing, a new technology emerged from additive manufacturing (3D printing), is widely known for its capability of programming post-fabrication shape-changing into artifacts. Fused deposition modeling (FDM)-based 4D printing, in particular, uses thermoplastics to produce artifacts and requires computational analysis to assist the design processes of complex geometries. However, these artifacts are weak against structural loads, and the design quality can be limited by less accurate material models and numerical simulations. To address these issues, this paper propounds a composite structure design made of two materials - polylactic acid (PLA) and carbon fiber reinforced PLA (CFPLA) - to increase the structural strength of 4D printed artifacts and a workflow composed of several physical experiments and series of dynamic mechanical analysis (DMA) to characterize materials. We apply this workflow to 3D printed samples fabricated with different printed parameters to accurately characterize the materials and implement a sequential finite element analysis (FEA) to achieve accurate simulations. The accuracy of deformation induced by the triggering process is both computationally and experimentally verified with several creative design examples, and the 95% confidence interval of the accuracy is (0.972, 0.985). We believe the presented workflow is essential to the combination of geometry, material mechanism and design, and has various potential applications.

cs.CG↗

arXiv2020

SimuLearn: Fast and Accurate Simulator to Support Morphing Materials Design and Workflows

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.

cs.HC↗

arXiv2020

Tuned Hybrid Non-Uniform Subdivision Surfaces with Optimal Convergence Rates

This paper presents an enhanced version of our previous work, hybrid non-uniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introduce a parameter $λ$ ($\frac{1}{4}<λ<1$) to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid non-uniform subdivision (tHNUS). Our previous work corresponds to the case when $λ=\frac{1}{2}$. While introducing $λ$ in hybrid subdivision significantly complicates the theoretical proof of $G^1$ continuity around extraordinary vertices, reducing $λ$ can recover the optimal convergence rates when tuned hybrid subdivision functions are used as a basis in isogeometric analysis. From the geometric point of view, the tHNUS retains comparable shape quality as [19] under non-uniform parameterization. Its basis functions are refinable and the geometric mapping stays invariant during refinement. Moreover, we prove that a tuned hybrid subdivision surface is globally $G^1$-continuous. From the analysis point of view, tHNUS basis functions form a non-negative partition of unity, are globally linearly independent, and their spline spaces are nested. We numerically demonstrate that tHNUS basis functions can achieve optimal convergence rates for the Poisson's problem with non-uniform parameterization around extraordinary vertices.

math.NA↗

arXiv2020

The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics

We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C^2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C^1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids is a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods.

physics.flu-dyn↗