CDS&E: Efficient Uncertainty Analysis in Multi-physics Phase Field Models of Microstructure Evolution

材料基因组计划通过模拟具有许多可能输入参数（成分、加工等）的材料，加速了材料设计。以便预测将产生所需性质（例如，用于冷却应用的更有效的热电体）的那些组合。 在任何这样的设计周期中，都存在输入的不确定性，重要的是要了解这些不确定性如何传播到输出属性的不确定性。 对于复杂计算，传统上用随机（“蒙特-卡罗”）采样来估计不确定性传播，但是当每次计算花费大量计算机时间时，这种采样变得过于昂贵。 该项目的一个主要成果是开发和公开发布有效的软件，以传播计算材料科学计算的不确定性。 虽然重点将放在材料微观结构演变的模拟上，但所提出的框架将适用于广泛的材料科学相关建模工具。还将开展活动以扩大项目的影响。 其中包括生成一个广泛的2D和3D微结构库，可用作模型系统来教授和开发微结构信息学的新框架，创建一个微结构动物园公民科学平台，以帮助标记和注释该项目中创建的合成微结构，以及创建跨学科的培训工具，用于计算材料科学中的不确定性量化。 该奖项还将支持两名研究生在材料科学和统计分析的接口培训。Technical SummaryThe Objective of this research is to create sequentially optimal sampling policies for propagation of uncertainty from model input to model outputs.这里考虑的问题是，进行准确和有效的不确定性传播时，面对计算昂贵的模型，特别是相场模型的热电和其他材料的微观结构演变。 在这项研究中，昂贵是指模型的资源将只允许为了10模型评估之前，需要作出决定的不确定性分析。这种模型在许多领域都很普遍，尽管这里的重点将放在计算材料科学应用上。 具体而言，在该项目中，研究团队将展示不确定性在CALPHAD相场模型链中的有效传播，该模型试图描述材料在化学和弹性驱动力下的微观结构演变。这些模型往往是高度不规则的，因为模型输出可以根据被采样的输入/参数空间中的区域而定性地不同。 此外，它们在计算上是昂贵的，模拟的完全三维实现需要超过10，000 CPU小时。此外，输入/参数空间通常是高维的，具有20多个随机输入条件和模型参数。这种不确定性传播框架的主要特征之一是它是非侵入性的，因为它作用于模型的输入空间。因此，唯一需要的信息是输入参数的联合概率分布，这使得该框架广泛适用，超出了用于开发它的特定测试问题（S）。该框架能够重新加权先前执行的模型评估，以最大限度地提高效率，不确定性传播，可以忽略不计的额外计算费用。 PI将通过开放许可证下的Github存储库发布不确定性传播和相位字段代码。 他们将建立一个公共的材料模型和数据管理系统（MMDMS），使他们在研究过程中产生的相场和DFT数据广泛可用，并与其他数据库协调。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

Nontechnical SummaryMaterials design has been accelerated under the Materials-Genome Initiative by simulating materials with many possible input parameters (composition, processing, etc.) in order to predict those combinations that will yield desired properties, for example, more efficient thermoelectrics for cooling applications. In any such design cycle, there are uncertainties in the inputs, and it is important to understand how these uncertainties propagate to uncertainties in the output properties. For complex computations, uncertainty propagation has traditionally been estimated with random ("Monte-Carlo") sampling, but when each calculation takes substantial computer time, such sampling becomes prohibitively expensive. A major outcome of this project is the development and public release of efficient software to propagate uncertainty across computational materials-science calculations. While the focus will be on simulations of the evolution of materials microstructures, the proposed framework will be applicable to a wide range of materials-science-relevant modeling tools. Activities will also be conducted to increase the impact of the project. These include the generation of an extensive library of 2D and 3D microstructures that can be used as model systems to teach and develop new frameworks for microstructure informatics, the creation of a microstructure-zoo citizen-science platform to assist in labeling and annotating synthetic microstructures created in this project, and the creation of interdisciplinary training tools for uncertainty quantification in computational materials science. This award will also support the training of two graduate students at the interface of materials science and statistical analysis.Technical SummaryThe objective of this research is to create sequentially optimal sampling policies for the propagation of uncertainty from model inputs to model outputs. The problem considered here is that of conducting accurate and efficient uncertainty propagation when faced with computationally expensive models, specifically phase-field models of microstructure evolution in thermoelectrics and other materials. Expensive in this research refers to models for which resources will only permit order 10 model evaluations prior to the need to make a decision informed by the uncertainty analysis. Such models are prevalent in many fields, though the focus here will be on computational materials-science applications. Specifically, in this project, the research team will demonstrate the efficient propagation of uncertainty across CALPHAD-Phase Field Model chains that attempt to describe the microstructure evolution of materials under chemical and elastic driving forces. These models tend to be highly non-regular in that the model output can differ qualitatively depending on the region in the input/parameter space being sampled. Moreover, they are computationally expensive, with full three-dimensional realizations of the simulations requiring upwards of 10,000 CPU-hours. In addition, the input/parameter space is often high dimensional, with more than 20 stochastic input conditions and model parameters. One of the main features of this uncertainty propagation framework is that it is non-intrusive, as it works on the input space of the models. Thus, the only information needed is the joint probability distribution of the input parameters, which makes the framework widely applicable, beyond the specific test problem(s) used to develop it. The framework is capable of reweighting previously executed model evaluations in order to maximize efficiency for uncertainty propagation with negligible additional computational expense. The PIs will release uncertainty-propagation and phase-field code through a Github repository under open licenses. They will set up a public Materials Models and Data Management System (MMDMS) to make the phase-field and DFT data they generate in the course of this research widely available and coordinate with other data repositories.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.