在材料設(shè)計(jì)應(yīng)用中，通常使用復(fù)雜的計(jì)算模型和/或?qū)嶒?yàn)以更好理解材料系統(tǒng)或提高其性能。然而，高保真模型通常呈現(xiàn)出高度的非線性，其行為等效于一個(gè)黑盒，這阻礙了輸入–輸出關(guān)聯(lián)性之外的直觀理解。

與此同時(shí)，實(shí)驗(yàn)本質(zhì)上也是黑盒，這是因?yàn)檩斎耄ㄈ缁瘜W(xué)、加工方案）和輸出（即性能或性能指標(biāo)）之間的中間聯(lián)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(shù)據(jù)高效的方法，以有效應(yīng)對這些挑戰(zhàn)，同時(shí)保證發(fā)現(xiàn)和/或設(shè)計(jì)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(yōu)化（BO）由于能夠以最小的數(shù)據(jù)集運(yùn)行而在材料設(shè)計(jì)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(shù)據(jù)形式的統(tǒng)計(jì)信息。實(shí)際上，設(shè)計(jì)者通常掌握支配材料系統(tǒng)的底層物理定律，利用這部分信息可能會(huì)提高優(yōu)化過程的效率和速度。

來自德州農(nóng)工大學(xué)材料科學(xué)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(xué)引入高斯過程（GP）核，以探索材料系統(tǒng)設(shè)計(jì)中潛在的效率提升和最優(yōu)工藝參數(shù)。

題目的方法結(jié)合了傳統(tǒng)BO技術(shù)的優(yōu)勢，以及使用已知的控制方程進(jìn)行物理建模的優(yōu)點(diǎn)。通過向統(tǒng)計(jì)信息中注入理論見解，增強(qiáng)了GP的概率建模能力，從而降低了數(shù)據(jù)依賴性，并更快地收斂到最優(yōu)設(shè)計(jì)。

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

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

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

這項(xiàng)工作為BO框架中物理注入內(nèi)核設(shè)計(jì)的應(yīng)用奠定了基礎(chǔ)，為各種材料科學(xué)應(yīng)用開辟了新的可能性。該文近期發(fā)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(shè)計(jì)中基于物理信息的貝葉斯優(yōu)化方法：應(yīng)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(shè)計(jì)和最優(yōu)工藝參數(shù)的確定是一項(xiàng)復(fù)雜且有挑戰(zhàn)性的任務(wù)，需要高效利用現(xiàn)有的數(shù)據(jù)。貝葉斯優(yōu)化（BO）由于其能夠以最小的數(shù)據(jù)集運(yùn)行而在材料設(shè)計(jì)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(shù)據(jù)形式的統(tǒng)計(jì)信息，并將目標(biāo)函數(shù)視為黑盒。實(shí)際上，設(shè)計(jì)者通常掌握支配材料系統(tǒng)的底層物理定律，這使得目標(biāo)函數(shù)并不完全是黑盒，因?yàn)橐恍┬畔⑹遣糠挚捎^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(nèi)核，有效利用決策過程中的統(tǒng)計(jì)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(shí)現(xiàn)數(shù)據(jù)效率更高的BO。通過設(shè)計(jì)NiTi形狀記憶合金，展示了該方法的適用性，確定了最大化轉(zhuǎn)變溫度所需的最優(yōu)工藝參數(shù)。