CAREER: A Stochastic Framework for Uncertainty Quantification on Complex Geometries: Application to Additive Manufacturing

职业：复杂几何形状不确定性量化的随机框架：在增材制造中的应用

• 批准号: 1942928
• 负责人: Johann Guilleminot
• 金额: $ 56.32万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-02-01 至 2025-01-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1942928&HistoricalAwards=false
• 关键词: CAREER; Stochastic; Framework; Uncertainty; Quantification

This Faculty Early Career Development (CAREER) grant will support fundamental research focusing on the integration of complex geometries in predictive stochastic computational modeling. Recent technological breakthroughs in, e.g., additive manufacturing and tissue engineering, have revolutionized the way materials and structures are processed, fabricated, and manufactured. By enabling the production of parts with unprecedented levels of material and geometric complexities over multiple length scales, these breakthroughs have also greatly enhanced the challenges in computational modeling and experimental testing. One of them is the quantification of part response uncertainties over complex geometries. This CAREER project aims to develop a stochastic modeling framework that will enable the automatic and robust integration of complex geometrical features into high-dimensional, predictive computational settings. This approach will pave the way for theoretical developments and virtual testing paradigms in fields where uncertainty in behavior must be quantified on real-world geometries. As part of the project, an extensive educational and outreach plan is also planned. This component notably includes: (1) hands-on research opportunities for undergraduate and graduate students, (2) activities to engage and educate a broad audience on basic science concepts with impactful applications, and (3) activities to increase the participation of K-12 students and underrepresented groups in computational mechanics, materials science, and STEM at large. This research seeks to bridge the gap between geometrical complexity and uncertainty quantification methodologies. While there has been considerable progress in the development of probabilistic frameworks accounting for multiple sources of uncertainties in computational physics, the proper integration of complex (e.g., nonconvex) geometrical descriptions into stochastic approaches remains mostly unexplored. In this case, the characteristics of the geometrical features and the intrinsic properties of material uncertainties are intertwined through processing conditions, which uniquely challenges the state-of-the-art in stochastic modeling and uncertainty quantification. To advance new knowledge and tools, the objectives of this project include: (1) the development of appropriate probabilistic representations for a broad class of stochastic constitutive models across (spatial) scales, (2) the construction of efficient generators for sampling on complex large-scale domains, and (3) the development of robust probabilistic methodologies for model identification, propagation, and validation. To address these issues, the research will combine theoretical derivations for stochastic modeling on constrained state spaces, computational developments for random generation through fractional partial differential equations, Bayesian inference for underdetermined statistical inverse problems, and experimental characterization on additively-manufactured bone-like titanium scaffolds.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这项教师早期职业发展（职业）赠款将支持基础研究，重点是在预测性随机计算建模中的复杂几何形状整合。最近的技术突破，例如添加剂制造和组织工程，彻底改变了对材料和结构的处理，制造和制造的方式。通过在多个长度尺度上启用具有前所未有的材料和几何复杂性水平的零件，这些突破也大大提高了计算建模和实验测试的挑战。其中之一是对复杂几何形状的零件响应不确定性进行定量。该职业项目旨在开发一个随机建模框架，该框架将使复杂的几何特征自动整合到高维，预测的计算设置中。这种方法将为必须在实际几何形状上量化行为不确定性的领域中的理论发展和虚拟测试范例铺平道路。作为该项目的一部分，还计划了一项广泛的教育和外展计划。该组成部分特别包括：（1）本科生和研究生的动手研究机会，（2）活动的活动，使广泛的受众了解具有影响力应用的基础科学概念，以及（3）增加K-12学生和代表性不足的群体在计算机制，材料科学和大部分词干中的活动。这项研究旨在弥合几何复杂性和不确定性定量方法之间的差距。尽管概率框架的发展取得了很大的进步，这些框架构成了计算物理学中多种不确定性来源的发展，但复杂（例如，非convex）的几何描述的正确整合到随机方法中仍然主要是无法探索的。在这种情况下，几何特征的特征和物质不确定性的内在特性通过处理条件交织在一起，这在随机建模和不确定性量化方面唯一挑战了最新的。 To advance new knowledge and tools, the objectives of this project include: (1) the development of appropriate probabilistic representations for a broad class of stochastic constitutive models across (spatial) scales, (2) the construction of efficient generators for sampling on complex large-scale domains, and (3) the development of robust probabilistic methodologies for model identification, propagation, and validation.为了解决这些问题，该研究将结合理论推导在约束状态空间上进行随机建模的理论推导，通过分数部分微分方程的随机生成的计算发展，贝叶斯对不确定的统计逆问题的推断以及实验性表征以及对成型骨骼造成的滴定奖的构成质量的构成奖，并通过构成的质量奖励进行了反映，并在nsf的质量上进行了实验表征。智力优点和更广泛的影响审查标准。

项目成果

Polyconvex neural networks for hyperelastic constitutive models: A rectification approach

用于超弹性本构模型的多凸神经网络：一种校正方法

• DOI: 10.1016/j.mechrescom.2022.103993
• 发表时间: 2022
• 期刊: Mechanics Research Communications
• 影响因子: 2.4
• 作者: Chen, Peiyi;Guilleminot, Johann
• 通讯作者: Guilleminot, Johann

A Riemannian stochastic representation for quantifying model uncertainties in molecular dynamics simulations

• DOI: 10.1016/j.cma.2022.115702
• 发表时间: 2022-07
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Hao Zhang;J. Guilleminot

Representing model uncertainties in brittle fracture simulations

• DOI: 10.1016/j.cma.2023.116575
• 发表时间: 2024-01
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Hao Zhang;J. Dolbow;Johann Guilleminot

Stochastic Modeling and identification of material parameters on structures produced by additive manufacturing

增材制造结构材料参数的随机建模和识别

• DOI: 10.1016/j.cma.2021.114166
• 发表时间: 2021
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Chu, Shanshan;Guilleminot, Johann;Kelly, Cambre;Abar, Bijan;Gall, Ken
• 通讯作者: Gall, Ken

Uncertainty quantification of TMS simulations considering MRI segmentation errors

考虑 MRI 分割误差的 TMS 模拟的不确定性量化

• DOI: 10.1088/1741-2552/ac5586
• 发表时间: 2022
• 期刊: Journal of Neural Engineering
• 影响因子: 4
• 作者: Zhang, Hao;Gomez, Luis J;Guilleminot, Johann
• 通讯作者: Guilleminot, Johann