在材料設計應用中，通常使用復雜的計算模型和/或實驗以更好理解材料系統或提高其性能。然而，高保真模型通常呈現出高度的非線性，其行為等效于一個黑盒，這阻礙了輸入–輸出關聯性之外的直觀理解。

與此同時，實驗本質上也是黑盒，這是因為輸入（如化學、加工方案）和輸出（即性能或性能指標）之間的中間聯系往往只能用隱式的方式來解釋。因此，人們亟需一種新的數據高效的方法，以有效應對這些挑戰，同時保證發現和/或設計過程的可理解性和高效性。

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

貝葉斯優化（BO）由于能夠以最小的數據集運行而在材料設計中廣受歡迎。然而，許多基于BO的框架主要依賴于輸入–輸出數據形式的統計信息。實際上，設計者通常掌握支配材料系統的底層物理定律，利用這部分信息可能會提高優化過程的效率和速度。

來自德州農工大學材料科學與工程系的Danial Khatamsaz等，提出了一套基于物理信息的BO框架。該框架將物理學引入高斯過程（GP）核，以探索材料系統設計中潛在的效率提升和最優工藝參數。

題目的方法結合了傳統BO技術的優勢，以及使用已知的控制方程進行物理建模的優點。通過向統計信息中注入理論見解，增強了GP的概率建模能力，從而降低了數據依賴性，并更快地收斂到最優設計。

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

物理知識的結合不僅提高了BO框架的性能，而且允許對支配系統的底層物理有更深入的理解，從而做出更明智、更高效的設計決策。研究者通過設計NiTi形狀記憶合金，展示了該方法的適用性，確定了最大化轉變溫度所需的最優工藝參數。

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

這項工作為BO框架中物理注入內核設計的應用奠定了基礎，為各種材料科學應用開辟了新的可能性。該文近期發布于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及其翻譯

A physics informed bayesian optimization approach for material design: application to NiTi shape memory alloys?(材料設計中基于物理信息的貝葉斯優化方法：應用于NiTi形狀記憶合金)

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?材料的設計和最優工藝參數的確定是一項復雜且有挑戰性的任務，需要高效利用現有的數據。貝葉斯優化（BO）由于其能夠以最小的數據集運行而在材料設計中廣受歡迎。然而，許多基于BO的框架主要依賴于輸入–輸出數據形式的統計信息，并將目標函數視為黑盒。實際上，設計者通常掌握支配材料系統的底層物理定律，這使得目標函數并不完全是黑盒，因為一些信息是部分可觀測的。在本研究中，我們提出了一種基于物理信息的BO方法，它通過集成物理注入的內核，有效利用決策過程中的統計信息和物理信息。我們證明了該方法能夠顯著提高決策效率，實現數據效率更高的BO。通過設計NiTi形狀記憶合金，展示了該方法的適用性，確定了最大化轉變溫度所需的最優工藝參數。