基于物理信息的贝叶斯优化方法

在材料设计应用中，通常使用复杂的计算模型和/或实验以更好理解材料系统或提高其性能。然而，高保真模型通常呈现出高度的非线性，其行为等效于一个黑盒，这阻碍了输入–输出关联性之外的直观理解。

与此同时，实验本质上也是黑盒，这是因为输入（如化学、加工方案）和输出（即性能或性能指标）之间的中间联系往往只能用隐式的方式来解释。因此，人们亟需一种新的数据高效的方法，以有效应对这些挑战，同时保证发现和/或设计过程的可理解性和高效性。

Fig. 2 Comparison of physics-informed and black-box modeling of Eq. (1).

贝叶斯优化（BO）由于能够以最小的数据集运行而在材料设计中广受欢迎。然而，许多基于BO的框架主要依赖于输入–输出数据形式的统计信息。实际上，设计者通常掌握支配材料系统的底层物理定律，利用这部分信息可能会提高优化过程的效率和速度。

来自德州农工大学材料科学与工程系的Danial Khatamsaz等，提出了一套基于物理信息的BO框架。该框架将物理学引入高斯过程（GP）核，以探索材料系统设计中潜在的效率提升和最优工艺参数。

题目的方法结合了传统BO技术的优势，以及使用已知的控制方程进行物理建模的优点。通过向统计信息中注入理论见解，增强了GP的概率建模能力，从而降低了数据依赖性，并更快地收敛到最优设计。

Fig. 5 The solutions corresponding to maximum transformation temperature in all 50 replications of simulations.

物理知识的结合不仅提高了BO框架的性能，而且允许对支配系统的底层物理有更深入的理解，从而做出更明智、更高效的设计决策。研究者通过设计NiTi形状记忆合金，展示了该方法的适用性，确定了最大化转变温度所需的最优工艺参数。

Fig. 6 Volume fraction and mean inter-particle distance of discovered sets of solutions shown in Fig. 5.

这项工作为BO框架中物理注入内核设计的应用奠定了基础，为各种材料科学应用开辟了新的可能性。该文近期发布于npj Computational Materials 9: 221 (2023).

Fig. 7 Optimal solutions discovered by physics-informed and black-box BO scenarios.

Editorial Summary

In material design applications, complex computational models and/or experiments are employed to gain a better understanding of the material system or to improve its performance. High-fidelity models, however, often exhibit high non-linearity, effectively behaving as black-boxes that hinder intuitive understanding beyond input-output correlations. At the same time, experiments are inherently black-box in nature as intermediate linkages between inputs (e.g. chemistry, processing protocols) and outputs (i.e. properties or performance metrics) tend to be accounted for only in an implicit manner. There is thus a growing need for novel data-efficient approaches that can effectively address these challenges while ensuring that the discovery and/or design process remains comprehensible and effective. Bayesian Optimization (BO) has gained popularity in materials design due to its ability to work with minimal data. However, many BO-based frameworks predominantly rely on statistical information, in the form of input-output data. In practice, designers often possess knowledge of the underlying physical laws governing a material system. Leveraging this partial information could potentially bolster the optimization process’s efficiency and speed. 

Danial Khatamsaz et al. from the Materials Science and Engineering Department, Texas A&M University, proposed a physics-informed BO framework. This framework introduces physics into the Gaussian Process (GP) kernel to explore potential efficiency enhancements in material system design and the discovery of optimal processing parameters. The proposed approach combines the advantages of traditional BO techniques with the benefits of employing known governing equations for physical modeling. By infusing statistical information with theoretical insights, they strengthened the GP’s probabilistic modeling capability, resulting in reduced data dependency and faster convergence to the optimal design. The incorporation of physical knowledge not only improves the performance of BO frameworks, but also allows for a deeper understanding of the underlying physics governing the system, which can lead to more informed and efficient design decisions. The applicability of this approach is showcased through the design of NiTi shape memory alloys, where the optimal processing parameters are identified to maximize the transformation temperature. This work lays a foundation for the application of physics-infused kernel design within the BO framework, opening up new possibilities across various materials science applications. This article was recently published in npj Computational Materials 9: 221 (2023).

原文Abstract及其翻译

A physics informed bayesian optimization approach for material design: application to NiTi shape memory alloys (材料设计中基于物理信息的贝叶斯优化方法：应用于NiTi形状记忆合金)

Danial Khatamsaz,Raymond Neuberger, Arunabha M. Roy, Sina Hossein Zadeh, Richard Otis & Raymundo Arróyave 

Abstract The design of materials and identification of optimal processing parameters constitute a complex and challenging task, necessitating efficient utilization of available data. Bayesian Optimization (BO) has gained popularity in materials design due to its ability to work with minimal data. However, many BO-based frameworks predominantly rely on statistical information, in the form of input-output data, and assume black-box objective functions. In practice, designers often possess knowledge of the underlying physical laws governing a material system, rendering the objective function not entirely black-box, as some information is partially observable. In this study, we propose a physics-informed BO approach that integrates physics-infused kernels to effectively leverage both statistical and physical information in the decision-making process. We demonstrate that this method significantly improves decision-making efficiency and enables more data-efficient BO. The applicability of this approach is showcased through the design of NiTi shape memory alloys, where the optimal processing parameters are identified to maximize the transformation temperature.

摘要 材料的设计和最优工艺参数的确定是一项复杂且有挑战性的任务，需要高效利用现有的数据。贝叶斯优化（BO）由于其能够以最小的数据集运行而在材料设计中广受欢迎。然而，许多基于BO的框架主要依赖于输入–输出数据形式的统计信息，并将目标函数视为黑盒。实际上，设计者通常掌握支配材料系统的底层物理定律，这使得目标函数并不完全是黑盒，因为一些信息是部分可观测的。在本研究中，我们提出了一种基于物理信息的BO方法，它通过集成物理注入的内核，有效利用决策过程中的统计信息和物理信息。我们证明了该方法能够显著提高决策效率，实现数据效率更高的BO。通过设计NiTi形状记忆合金，展示了该方法的适用性，确定了最大化转变温度所需的最优工艺参数。