力学进展, 2021, 51(1): 82-105 DOI: 10.6052/1000-0992-20-012

研究综述

基于仿真和数据驱动的先进结构材料设计

李想1,2, 严子铭1, 柳占立,1,*, 庄茁1

1 清华大学航天航空学院, 应用力学教育部重点实验室, 北京 100084

2 海南师范大学信息科学技术学院, 海口 570206

Advanced structural material design based on simulation and data-driven method

LI Xiang1,2, YAN Ziming1, LIU Zhanli,1,*, ZHUANG Zhuo1

1 Applied Mechanics Lab., Dept. of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China

2 School of Information Science and Technology, Hainan Normal University, Haikou 570206, China

通讯作者: *E-mail:liuzhanli@tsinghua.edu.cn

柳占立, 男, 1981年出生, 清华大学航天航空学院长聘副教授、博导. 2004、2009年在清华大学工程力学系获学士和博士学位, 从2009年至2012年在美国西北大学机械工程系从事博士后研究. 现任清华大学航天航空学院工程力学系副主任, 中国力学学会计算力学专委会副主任, 国际期刊《International Journal of Fracture》Regional Editor. 主要围绕固体强度与断裂的数值仿真和工程设计开展研究, 包括爆炸冲击下结构动态失效和人体致伤机制分析、新型防护装备设计、基于机器学习的计算力学及反向工程设计等. 研究成果应用于爆炸冲击波防护装备研制、页岩水力压裂施工设计、飞行器穿盖弹射救生等国家重大工程. 在《JMPS》《IJSS》《CMAME》《IJNME》等力学期刊发表学术论文100余篇, 出版中英文专著3部. 2011年教育部全国百篇优秀博士论文获得者, 2015年获中国力学青年科技奖, 2017年获基金委优秀青年基金支持, 2018年获教育部自然科学奖一等奖(排名2), 2020年获钱令希计算力学青年奖.

收稿日期: 2020-05-29   接受日期: 2020-09-29   网络出版日期: 2021-03-25

Corresponding authors: *E-mail:liuzhanli@tsinghua.edu.cn

Received: 2020-05-29   Accepted: 2020-09-29   Online: 2021-03-25

作者简介 About authors

摘要

先进结构材料近年来受到材料和结构设计领域的广泛关注, 这些材料一般通过多个尺度的结构设计实现各种卓越的性能. 在早期的材料设计中, 有的基于设计者的丰富经验, 从天然拓扑结构中抽象出合理的数学力学模型; 有的基于生物系统的结构和功能特点提取出仿生力学模型. 然而, 仅依靠经验性的巧妙设计很难得到最优的设计方案, 通过反复迭代设计和试验来遍历设计空间也不切实际. 为此, 拓扑优化方法被成功应用于声子晶体、元胞材料等先进结构材料的优化设计中, 但现有的拓扑优化方法在实现精准的反向设计方面尚存挑战. 基于数据驱动的机器学习方法擅长建立数据空间多维变量复杂关系, 能够揭示传统力学研究方法难以发现的更深层次的力学机理和规律, 成为力学领域崭新的研究热点. 本文系统地回顾先进结构材料设计方法的发展历程, 对比阐述各种主流设计方法, 结合本课题组的相关工作介绍数值仿真和数据驱动在先进结构材料的智能化设计方面的应用现状, 并对该领域的未来研究趋势进行探讨和展望.

关键词: 结构材料 ; 超材料 ; 材料设计 ; 数据驱动 ; 机器学习

Abstract

Advanced structural materials have received extensive attention in the field of materials and structural design in recent years. These materials generally achieve excellent performances via structural design at multiple length-scales. In the early material design, some researchers created reasonable mathematical and mechanical models from the natural topologies; some researchers established bionic mechanical models based on the structural and functional characteristics of biological systems. Nevertheless, it isn't easy to obtain the optimal designs only based on ingenious design. To traverse the design space to search for the optimal design by trial and error is also not practical. For these reasons, the topology optimization method has been successfully applied to the design of advanced structural materials such as phononic crystals, cellular materials, etc. However, the existing topology optimization methods still have challenges in achieving accurate reverse designs. Data-driven methods can establish complex relationships of multi-dimensional variables, and they can reveal mechanical mechanisms and laws that are difficult to be discovered by traditional methods. Hence, this paper systematically reviews the development of advanced structural material design methods. Various mainstream design methods are compared and illustrated. The status of intelligent design of advanced structural materials based on data-driven methods is introduced. The prospect of this research area is discussed.

Keywords: structural materials ; metamaterials ; material design ; data-driven ; machine learning

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本文引用格式

李想, 严子铭, 柳占立, 庄茁. 基于仿真和数据驱动的先进结构材料设计. 力学进展[J], 2021, 51(1): 82-105 DOI:10.6052/1000-0992-20-012

LI Xiang, YAN Ziming, LIU Zhanli, ZHUANG Zhuo. Advanced structural material design based on simulation and data-driven method. Advances in Mechanics[J], 2021, 51(1): 82-105 DOI:10.6052/1000-0992-20-012

1 引言

材料的力学性质是材料学领域的研究核心内容之一. 近年来出现的先进结构材料等人工复合材料可通过多尺度的结构设计实现各种的卓越的力学性能, 因而受到研究人员的广泛关注. 常见的先进结构材料有包含点阵结构在内的以高比性能为核心的元胞材料和满足各种特殊性能需求的功能性超材料等.

大自然可以通过生物组织的进化创造出具有优良力学性能的天然元胞材料 (Zheng et al. 2014), 其一般包括蜂窝结构和泡沫结构等基本形式, 如图1(a)和 图1(b)所示. 天然元胞材料可以实现超低密度、应变隔离、能量吸收、裂纹俘获(crack arrest)、热交换、流体存储与交换、过滤等功能. 受天然元胞材料的启发, 研究者提出了人工元胞材料的概念. 人工元胞材料继承了天然元胞材料的诸多优点. 图1(c)和 图1(d)给出了典型的人工元胞的结构形式. 通过周期性元胞构成的材料或结构可以实现优良的比刚度 (Chu et al. 2008)和比强度 (Bauer et al. 2014)等. 近年来, Cheung和Gershenfeld (2013)提出了一种可重组式新型元胞材料, 如图 1(f)所示. 该材料可以通过元胞的装配实现优异的比模量和比强度, 受到航天航空领域的关注.

图1

图1   代表性天然元胞材料与人工元胞材料. (a)天然蜂窝型元胞材料, (b) 亚马逊睡莲叶表面脉络型元胞材料 (Mcnulty et al. 2017), (c) 人工八角形桁架元胞材料 (Zheng et al. 2014), (d) 曲壳形元胞材料 (Han et al. 2015), (e) 基于空间填充棱柱的可重组式人工元胞材料 (Overvelde et al. 2017), (f)点阵型可重组式人工元胞材料 (Cheung & Gershenfeld 2013)


微纳米力学结构超材料(micro/nano-structured mechanical metamaterials)是近年来材料研究的前沿领域. 这些材料一般通过微观或纳观尺度的结构设计, 实现天然材料不具备的特殊力学性能, 如图2 所示. 例如, 力学结构超材料具有优异的比性能, 其等效比模量与所包含的天然材料之间存在平方甚至立方关系 (Gibson & Ashby 1982). 这类材料还可以通过巧妙的结构设计实现超低密度 (Han et al. 2015)和负泊松比 (Choi & Lakes 1992)等力学性能, 如图2(a)所示. 此外, 由金属或聚合物构成的多孔力学结构超材料在碰撞或冲击下其内部结构通过塑性变形耗散能量, 体现出优异的能量吸收特性 (Lefebvre et al. 2008), 如图2(b)所示.

图2

图2   常见的功能结构超材料: (a) 负泊松比超材料 (Bückmann et al. 2012); (b) 抗冲击超材料 (Han et al. 2015); (c)光子晶体 (Digaum et al. 2014); (d) 声子晶体 (Mohammadi et al. 2008)


在多种超材料中, 光子晶体为控制光的传播提供了可能性, 在通讯、激光器和光子原件中具有广阔的应用前景. 基于变换声学的概念, 某些特定情况下电磁学的基本方程与弹性动力学的基本方程是等价的. 因此, 较早出现的各类型光子晶体的原理与设计方法为发展对机械波进行调控的力学结构超材料提供了诸多借鉴价值. 光子晶体是由具有不同折射率的介质所组成的周期性人工材料, 如图2(c)所示, 其相关研究可以追朔到18世纪. 1887年, Rayleigh (1888)发现一维多层半导体的材料对某个波长范围的电磁波具有很大的反射率. 1987年, Yablonovitch (1987)John (1987)分别讨论了高维度的周期性光学结构的性质, 并明确提出了光子晶体的概念. 光子晶体的一个重要特性是光子带隙, 指的是该频率范围内的输入会发生全反射, 从而无法穿过光子晶体材料. 带隙的存在催生了一系列的光子晶体的应用. 例如, 可以通过在光子晶体中引入缺陷结构制造滤波器 (N$\check{e}$mec et al. 1). 另外, 可进一步依靠光子晶体内部的缺陷引导光的传播方向, 实现光子晶体的波导功能 (Vlasov et al. 2005). 基于光子晶体的带隙范围的变化可研制多功能、多物理场的传感器 (Sharma et al. 2004, Peterson et al. 2014), 对温度、离子浓度、金属含量等各种物理量进行探测. 通过改变电磁波的传播方向, 声子晶体材料还可以实现对可见光 (Ergin et al. 2010)、激光及红外线 (Wang et al. 2016)等的隐身.

通过类比对电磁波和机械波调控问题中的相似性, Kushwaha等 (1993)提出了声子晶体的这类力学结构超材料. 声子晶体是一种由周期性单胞构成的非均质人造材料. 单胞一般由散射体(或空隙)和基体组成, 如图2(d)所示. 声子晶体能够对声波和机械振动进行多方位的调控, 在减振降噪、滤波、声学透镜、声学成像、声隐身等方面有重要的应用价值, 受到通信、医疗、军事等领域的关注 (Sáchez-Dehesa et al. 2002, Ho et al. 2003, Wen et al. 2005). 早期声子晶体研究以散射型为主, 一般由两相材料构成. 2000年, Liu等 (2000)提出了"共振型声子晶体"的概念, 该概念后来演变为"声学超材料". 这类声子晶体通过在软基体中加入由硬核和涂层组成的微颗粒, 使微颗粒自身形成了弹簧振子结构吸收能量. 相比于散射型声子晶体, 共振型声子晶体能调控更低频率的声波和机械振动, 拓宽了声子晶体的应用领域. 在此基础上, Sánchez-Dehesa (2002)Hu等 (2004)又提出了负质量、负密度以及"双负材料"等概念, 对波的调控形式也从衰减幅值扩展到改变声波传播方向、负折射、声聚焦等等. 如何通过设计声子晶体以实现所需要的声波调控功能已成为近年来声子晶体研究的热点问题.

这些先进材料的出现对材料设计方法提出了更高的要求. 生物的天然元胞结构是亿万年演化的结构, 其元胞结构往往具备优良的力学性能. 因此, 早期的研究者在进行材料设计时通常基于自身的丰富经验, 从天然拓扑结构抽象出合理的数学力学模型; 有的研究者从生物系统的结构和对应功能中获取灵感, 总结出蕴含典型功能原理和作用机理的仿生模型. 但是, 仅依靠经验性的巧妙设计很难得到最优的设计方案, 而通过计算遍历所有可能的拓扑空间也显得不切实际. 为此, 研究者将拓扑优化方法应用于材料设计中. 拓扑优化方法可在指定的设计区域内寻找全新的材料分布以实现最佳的结构性能. 该方法在过去三十年来逐步衍生出密度法、水平集法、相场法、拓扑导数法、进化方法等分支 (Xie & Steven 1993, Allaire et al. 2002, Bourdin & Chambolle 2003). 拓扑优化方法已被成功应用于光子晶体 (Borel et al. 2004; Frandsen et al. 2004; Jensen & Sigmund 2004, 2005, 2011; Wang et al. 2011)、声子晶体 (Sigmund & Søndergaard Jensen 2003; Halkjær et al. 2005; Dong et al. 2014a, 2014b; Park et al. 2015; Dong et al. 2017a, 2017b; Zhang et al. 2018)、元胞材料 (Niu et al. 2009, Huang et al. 2011, Huang et al. 2013)等先进人工材料的结构设计. 但是, 现有的拓扑优化方法以优化设计为主, 而在实现精准的反向设计方面尚存挑战. 同时, 近年来材料制备工艺的发展也对设计方法提出了更高的要求. 如何精准、高效地进行材料反向设计将是未来材料研究领域的热点.

进入21世纪以来, 以深度学习和强化学习为代表的机器学习得到了空前发展, 相关成果逐渐被研究者应用至诸多科研领域. 在力学领域, 一般基于力学实验和数值模拟获取的大量数据, 利用机器学习算法能够建立高维变量复杂关系的优势, 挖掘传统力学方法难以发现的规律, 揭示更深层次的力学机理. 近年来, 机器学习方法在先进材料的智能化设计中逐渐崭露头角. 例如, 监督式机器学习使用带标签数据训练出可表征数据与标签之间隐式关系的黑盒模型, 被成功用于声学 (Li et al. 2020)、光学 (Malkiel et al. 2018)人工材料的反向设计. 无监督机器学习在缺乏足够先验知识的条件下, 对无类别信息的数据进行聚类或分群, 被用于材料微结构特征自动分类和材料拓扑特征降维压缩 (Li et al. 2019). 强化学习算法通过智能体在与环境的交互过程中不断更新算法策略, 最终实现全局最优或特定目标的实现, 已被应用于优化设计一维声学人工材料的结构 (Luo et al. 2020).

围绕上述各种先进材料, 本文将回顾先进结构材料设计方法的发展历程, 对比阐述各种主流设计方法, 其结构框图如图3所示. 首先介绍的是包括基于经验、仿生和拓扑优化在内的传统设计方法, 再结合课题组的相关工作介绍机器学习在先进结构材料的智能化、自动化设计方面的应用现状, 最后对该领域的未来研究方向进行探讨和展望.

图3

图3   先进结构材料设计方法框图


2 基于经验设计

结构材料的传统设计方法往往源自人类不断积累的生产生活经验, 结合一般性的物理规律, 归纳总结不同天然结构与人工结构的优缺点, 以获得各式各样具有特定性能目标的元胞或结构形式. 2001年, Dyskin等 (2001)通过互锁方式将四面体元胞组装成单层结构. Dyskin等 (2003)发现具有四面体、立方体、八面体、十二面体、二十面体中的任何一个的外部几何形状的元胞均可通过互锁方式组装形成单层结构. Overvelde等 (2017)从传统折纸技术中获得灵感, 基于空间填充棱柱形元胞设计和制造了三维可重组材料, 如图1(e)所示. Lipperman等 (2009)设计了由三角形和六边形元胞构成的周期性结构, 通过可变的元胞截面形状实现了良好的抑制裂纹扩展功能. Mirkhalaf和Barthelat (2017)设计出了具备双稳态互锁机构的结构材料. 该材料具备高韧性、高损伤极限以及可重复组装等优良的工程特性. Haghpanah等 (2016)通过巧妙设计铰接部件设计出具有多个稳态的可变形结构材料, 该材料可以在不影响结构完整性和使用寿命的情况下在多个稳态构型之间反复切换. 基于最小表面原理, Han等 (2015)设计了具有光滑曲面的曲壳形元胞材料, 并通过光刻技术制备了纳米级样本. 该材料在$10^{-2} {\rm Mg/m}^{3}$的密度水平具有优良的比刚度和强度. Cheung和Gershenfeld (2013)提出了一种可反向组装的新型复合元胞材料, 如图1(f)所示. 该材料利用互锁的连接机构将元胞组成宏观材料或结构, 具备优异的比刚度和比强度, 且装配工艺简单, 受到了航天领域的高度关注. 但是, 这类材料的宏观性能与元胞的连接装置之间存在很强的相关性, 尚未看到相关文献对此进行较全面地探讨. 另外, 这种材料的设计具有较强的经验性, 尚还未形成系统性的设计方法. Robert (1985)Larsen等 (1997)众多学者设计了具有负泊松比的人工元胞材料. Bertoldi (2017)利用不稳定性分别设计出力学系能可调的负泊松比材料、声学人工材料以及可反复使用的能量吸收材料. Choi和Lakes (1992)发展了具有等效负泊松比的多孔聚合物材料. Xu等 (1999)基于聚氨酯、聚偏二氟乙烯、环氧树脂等材料, 通过光刻技术制备了具有等效负泊松比的超材料. Wang等 (2009)研究了具有周期性微观结构的聚合物材料发生塑性变形时的吸能特性, 并基于数值仿真实现了吸能性能的优化. Lee等 (2010)通过实验研究了微、纳观尺度下的结构设计对环氧树脂抗冲击性能的影响.

早期的光子晶体设计主要依赖于经验. Liu等 (2005)依靠经验设计了基于光子晶体定向耦合器的紧凑型偏振分束器. Mutitu等 (2008)基于一维光子晶体设计了光捕(light trapping)装置, 可以反射短波长的光波$(400\sim 1100 $ nm), 同时透射具有更长波长的光波$(1100 \sim 1800 $ nm). Adibi等 (2000) 提出了一种设计光子晶体光波导的方法, 通过改变相邻空隙的尺寸可以调整高阶禁带的范围. Valentine等 (2008)利用级联"渔网"形结构制备了3D光学超材料, 实现了3.5的负折射率. Gabrielli等 (2009)通过空间变密度的纳观结构实现了微米尺度下的光学隐身.

声子晶体的设计一般从能带结构入手. 能带结构的示意图如图4(b)所示 (Mohammadi et al. 2008). 通过设计单胞可以使声子晶体对特定频率范围的声波具有反射效果, 从而使该频率范围内的声波大幅度衰减, 达到对声波的调控效果, 该频率范围称为"禁带" (Schriemer et al. 1997, Pennec & Djafari-Rouhani 2016, Srivastava 2019). 能带结构是不同波矢量下的波和其特征频率所组成的点的集合, 它可以通过取声子晶体元胞及附加周期性边界条件, 基于有限元等数值方法计算得到. 禁带的分布和宽度与声子晶体单胞的尺寸、材料密度、模量、散射体几何形状等参数均相关 (Pennec & Djafari-Rouhani 2016), 通过调控这些参数可以达到设计带隙的目的. 例如, Bertoldi等 (2013)通过大变形调控禁带. Huang等 (2012)通过设计弹簧振子结构来设计带隙. Krödel等 (2015)通过加入多种微颗粒从而达到拓宽禁带的目的. Nanthakumar等 (2019)基于量子自旋霍尔效应研究了声子晶体拓扑绝缘子的反向设计. Nguyen等 (2019)基于应变驱动机制设计了具有可调谐量子谷霍尔效应的声子晶体绝缘体的拓扑结构. 但目前尚难以通过解析方法给出设计参数和带隙特征的定量关系.

图4

图4   (a)声子晶体结构示意图 (Li et al. 2020), (b)色散曲线示意图 (Mohammadi et al. 2008)


基于经验的材料设计方法仍是当前最为普遍的设计方法, 并已获得了大量的研究成果. 但是, 这类研究方法往往需要抽象出合理的数学力学模型去解释设计原理, 并实现设计目标优化. 随着材料设计逐渐呈现出反问题设计、多物理场耦合及多目标设计以及主动可调性等特点, 解析的方法往往不足以胜任设计需求, 需要引入其他的设计方法进行补充.

3 基于仿生设计

自然界生物体经过万亿年的自然进化和选择, 完美地实现了天然材料的结构功能一体化, 产生了性能超越人类技术的天然元胞结构, 是丰富的材料信息库. 基于生物启发式思维, 人类通过对动植物的自然行为与功能的模仿, 研究各生物系统的结构和性质, 及其在不同外部环境下的表现, 提取出了蕴含典型功能原理和作用机理的生物模型, 结合人类的新技术、新材料, 通过结构与环境的协同演化, 能够实现最优化结构设计, 创造出仅凭人类经验难以设计出的高性能材料形式.

在具体实现途径上, 基于仿生的设计方法可分为两类: 一类通过提炼一般性力学模型, 对其特征参数进一步优化, 并通过适合的材料将其制备为具有特定功能的元胞材料. Wang (2009)Zhang和Ashby (1994)等研究了蜂窝及泡沫型元胞材料在能量吸收方面的性能. Scarpa等 (2003)研究了泡沫型非均匀元胞材料的动态力学响应, 探讨了其在振动控制方面的应用前景. Liu等 (2017)则总结了自然界中生物材料的功能梯度以及各向异性的基本设计形式和原理, 并讨论了如何将生物模型转化为可设计制造的高性能仿生材料. Speck等 (2013)受到植物微观元胞结构的启发, 研究了具有自愈合功能的聚合物材料. Zhang等 (2017) 通过设计分层的蜂窝微结构发展了具有超低密度、超高模量和强度的陶瓷/石墨烯超材料. Gu等 (2017)则通过仿生海螺壳的三维结果, 提出了该多层级天然材料的止裂机理, 制造出了抗冲击性能优异的多层级复合材料, 如图5所示; 另外, Gu等 (2016)通过对珍珠贝的抗冲击机理研究, 通过仿生其结构, 得到了抗冲击性能较好的层压板材料.

图5

图5   基于生物启发的多层级复合材料设计(Gu et al. 2017)


另一类则是在对生物模型研究的基础上, 直接对天然生物材料进行处理, 充分发挥自然材料本身的结构优点, 制造出衍生于母体的元胞材料. 胡良兵团队在该方向的工作获得了比较大的突破. Xu等 (2018)深入研究天然木材结构中微通道容纳气体以及细胞壁纳米通道容纳电解质的显著电化学特性, 同时经过处理, 使木基材料具备良好的柔韧性, 制造出了高容量、可用于柔性可穿戴电子设备的电池. Kong (2018)则利用天然木质纤维高拉伸强度, 各向异性性能突出以及水凝胶的柔韧性, 制备出了高各向异性、超高强度的可导电木质水凝胶, 实现了类似生物肌肉组织的功能. Wang等 (2017)利用醋杆菌沿细胞表面线性合成纤维素链, 获得了高抗拉强度和杨氏模量的大量纤维构件材料制备方法. Song等 (2018)则利用天然木材多孔, 纤维强度高的特性, 通过化学处理, 去除天然材料的木质素和半纤维素, 制备出了高比强度的超轻高性能木质材料.

当前, 仿生设计仍是结构材料设计的热门方法之一. 如何准确地在复杂环境系统下, 捕捉到生物结构优越力学性能所对应的作用机制和原理, 并抽象出高效、简单的生物力学模型, 是该领域的重点研究方向之一.

4 拓扑优化设计

传统设计往往需要结合丰富的理论知识和设计经验, 不断地筛选基本模型、调整模型参数, 并进行反复的试算、分析与校核, 才能得到符合设计预期的材料以及结构形式. 面对需要优化设计的场景, 传统设计则很难实现设计目标. 拓扑优化设计则是在相应的约束条件下, 借助可行的理论, 寻找材料或结构的最优设计方案, 与传统设计方法形成了良好的互补关系. 近年来, 拓扑优化方法被逐步应用于材料优化设计领域.

现代拓扑优化方法的核心思想是将需要优化的力学指标描述成与材料分布相关的函数, 通过各种优化算法迭代地逼近目标函数的最优解, 在一定约束条件下寻找到满足最优力学指标的材料分布形式, 实现材料或结构的优化设计. 拓扑优化方法已被普遍运用于元胞材料及光子、声子晶体等材料的优化设计.

拓扑优化方法被广泛用于探索具备优异准静态力学性能的元胞结构. Huang等 (2011)基于双向进化结构优化方法设计了具有最大体积模量和剪切模量的元胞结构. Niu等 (2009)发展了一种双尺度拓扑优化方法, 找到具有最大结构基频的蜂窝材料的宏观结构和微观结构. Carstensen等 (2015)将几何与材料非线性引入优化方程, 设计出具有最大能量吸收效率的蜂窝形元胞材料. Radman等 (2013)在传统双向进化结构优化(BESO)方法中引入随空间坐标非线性变化的优化目标, 成功设计出体积和剪切模量梯度变化的元胞材料.

早期的光子晶体设计主要依赖于研究者的经验. 近年来, 拓扑优化方法被成功应用于优化和设计光子晶体材料及设备的结构. Jensen和Sigmund (2004)基于拓扑优化设计了可将光路进行$90^\circ$偏折的声子晶体设备, 并将传输损耗(transmission loss)控制在3%以内. Borel等 (2004)基于拓扑优化反向设计了Z字型的光子晶体波导结构, 并通过实验验证所设计结构具有优良的传导率, 如图6(b)所示. Men等 (2014)使用拓扑优化对3维光子晶体的带隙范围进行了优化. Lin等 (2018)基于拓扑优化方法提出了多层光学超结构的设计框架, 实现了对相位角度的调控. Borel等 (2005)设计了Y型分光器, 通过拓扑优化实现了大频率范围内的低损耗率.

图6

图6   (a)一维、二维和三维光子晶体结构示意图; (b)基于拓扑优化方法设计的Z字型分光器 (Borel et al. 2004)


声子晶体材料的优化设计则一般从能带结构入手. 天津大学汪越胜教授团队开展了大量基于拓扑优化的声子晶体设计工作. 一部分工作关注各种声子晶体的设计, 优化设计了双相声子晶体、空隙声子晶体和"双负"声学人工材料 (Dong et al. 2014, 2017a, 2017b)等; 一部分工作关注算法上的创新, 如发展了基于遗传算法 (Dong et al. 2012)和具有多目标的优化函数 (Dong et al. 2014)的声子晶体拓扑优化方法. 大连理工亢战研究团队发展了声子晶体及拓扑优化方法, 围绕不确定性 (Zhang & Kang 2017, Zhang et al. 2018)、相场法 (Zhang et al. 2019a, 2019b)和定向传播 (He & Kang 2018)等问题开展了大量的工作. 此外, Halkjær (2005)等Sigmund等 (2003)Park等 (2015)等都基于拓扑优化进行声子晶体的设计.

拓扑优化设计提供了材料设计的新思路, 只需要在相应的约束条件下, 给定设计目标, 就可以生成传统经验无法设计出的高性能拓扑结构. 然而, 该类型材料设计方法受限于当前拓扑优化算法自身的局限性, 在动态问题设计目标和非线性问题优化函数的给定等问题上尚存挑战.

5 基于机器学习的智能结构材料设计

当前, 材料设计逐渐展现出极端载荷工况、多物理场耦合、多目标设计、系统集成以及主动可调性等特点, 传统设计方法往往难以实现上述目标, 需要引入新的理论去指导材料设计. 以拓扑优化为例, 该方法引入了诸如蚁群算法和粒子群算法等, 将拓扑优化和仿生概念相结合, 拓展了拓扑优化算法的丰富性. 近年来, 随着深度学习理论逐渐成熟, 人们发现该理论同样适用于指导材料设计, 并产生了一系列基于机器学习算法的智能化材料设计方法, 实现了传统方法难以实现的反向材料设计, 特别是对于无法解析表达的复杂材料和结构设计问题, 该类型算法表现出了相当大的优势.

5.1 机器学习发展历程

自20世纪80年代以来, 人工智能技术的蓬勃发展为实现先进结构材料的智能设计提供了可能. 约翰 $\cdot $ 麦肯锡 (1981)将人工智能定义为研究、开发用于模拟、延伸和扩展人的智能的理论、方法、技术及应用系统的一门新技术科学. 人工智能作为计算机科学的一个分支, 其目标是研究人类的思考、学习及工作方式, 并最终将研究成果转化为智能软件和计算机系统. 为开发出可以模仿人类思考和行为方式的智能软件和计算机系统, 1956年的达特茅斯会议正式提出了"人工智能"概念. 经过三十余年的发展, 人工智能从早期数学领域的应用逐步演化出人机对话系统、智能机器人、专家系统等. 然而, 这些人工智能模型大多需要人为指定程序逻辑, 不具备自我学习和更新的能力, 与真正意义上的智能相距甚远. 诸多原因导致传统人工智能的研究在20世纪80年代进入寒冬.

机器学习是实现人工智能的一种手段. 与早期的人工智能系统相比, 机器学习关注的是基于训练数据建立起计算模型, 而非通过编写程序实现特定逻辑, 如图7(a)所示. 自20世纪30年代起, 逐步诞生了线性判别器、朴素贝叶斯、线性回归、逻辑回归、感知机、K-近邻算法、支持向量机、自适应增强等机器学习模型.

图7

图7   (a)人工智能、机器学习与深度学习; (b)人工神经网络结构示意图


在众多方法中, 人工神经网络(artificial neural network, ANN)逐步发展成机器学习领域的一个重要分支, 其网络结构示意图如图7(b)所示. 人工神经网络的相关研究工作可以追溯到20世纪40年代. 1943年, McCulloch和Pitts (1943)受到生物神经活性特点的启发提出了人工神经元的数学模型. 1958年, Rosenblatt (1958)建立了感知机(perceptron)的模型, 该模型也被普遍认为是现代人工神经网络的前身. 1971年, Ivakhnenko (1971)首次提出了基于感知机的多层网络模型, 并在模型中应用了非线性多项式函数. 该算法后来逐步发展为现代深度神经网络的核心组成部分. 2006, Hinton和Salakhutdinov (2006)揭示出多层人工神经网络优秀的特征提取能力, 并可以通过逐层预训练的方式解决多层神经网络的训练难题, 开启了基于深度人工神经网络的"深度学习"时代.

经过十余年的快速发展, 深度学习已被成功应用于诸多领域. 例如, 在计算机视觉领域 (Cheng et al. 2015, Gatys et al. 2016, He et al. 2016, Redmon et al. 2016, Wen et al. 2016, Zhu et al. 2016)、语音处理和识别 (Xiong et al. 2016, Chiu et al. 2018)、自然语言处理领域 (Hermann et al. 2015, Gehring et al. 2017)、生命科学 (Webb 2018, AlQuraishi 2019)、制药 (Gawehn et al. 2016, Chen et al. 2018)、金融 (Heaton et al. 2017, Zhang et al. 2017)等诸多领域. 同时, 这股浪潮也延伸至工程及力学领域. 近年来, 机器学习及深度学习技术被逐步应用于岩石力学 (Fan et al. 1998, Zhou et al. 2004, Jin et al. 2006)、拓扑结构优化和设计 (Hajela & Lee 1995, Ohsaki 1995, Papadrakakis et al. 1998, Papadrakakis & Lagaros 2002, Gholizadeh et al. 2008, Lei et al. 2019)、边坡稳定性 (Xiating et al. 1995, Chen et al. 2001, Xia & Xiong 2004)、固体本构关系 (Furukawa & Yagawa 1998, Ghaboussi et al. 1998, Hashash et al. 2004, Jung & Ghaboussi 2006, Sun et al. 2010, Ji et al. 2011)、偏微分方程的数值求解 (Dissanayake & Phan-Thien 1994, Meade Jr & Fernandez 1994, Lagaris et al. 1998, Ramuhalli et al. 2005, Malek & Beidokhti 2006, Mehrkanoon & Suykens 2015, Anitescu et al. 2019)流体力学计算 (Faller & Schreck 1997, Mi et al. 2001, Butz & Von Stryk 2002, Wang & Liao 2004, Yuhong & Wenxin 2009, Beigzadeh & Rahimi 2012)等多个方向.

深度学习技术的本质是基于"联结主义"构建的多层非线性神经网络模型, 通过向后传播算法建立起不同维度的数据分布之间的映射, 挖掘出数据中蕴藏的潜在关联关系. 2014年诞生的生成对抗网络模型再次激发了学术界对深度学习的兴趣与期待. 生成对抗网络由生成器和判别器两个深度学习模型组成, 两个模型通过对抗式训练, 最终保证生成器网络将低维空间的噪音信号映射到与训练数据服从相同分布的高维度空间, 从而重建与原始样本接近的新样本 (Goodfellow et al. 2014). 生成对抗网络已被成功应用于谱曲 (Yang et al. 2017)、作画 (Liu et al. 2018)、作诗 (Rajeswar et al. 2017)等, 并在近年来逐步应用于自然科学研究. 在化学领域, 该模型被用于反向设计全新的无机 (Dan et al. 2019)和有机化合物 (Sanchez-Lengeling & Aspuru-Guzik 2018). 在生物领域被成功用于生成具有指定性质的DNA序列 (Killoran et al. 2017). 这些自然科学领域的成功应用对先进结构材料的智能设计具有重要指导意义. 此外, 由自动编码器所衍生出生成式深度学习模型同样受到自然科学领域研究者的关注. 自动编码器 (Ballard 1987, LeCun et al. 2015)是由编码器和解码器连接而成的深度学习模型, 其目标是通过无监督学习在模型输出端重现输入端数据, 实现数据降维. 降维后得到的特征数据还可进一步用于监督学习. 该模型常被应用于数据可视化降维、数据降噪和压缩等. 基于自动编码器还逐渐衍生出了变分自动编码器 (Kingma & Welling 2013)、对抗自动编码器 (Makhzani et al. 2015)等深度学习模型. 自动编码器的各种衍生模型已被应用于发现全新的药物分子结构 (Kadurin et al. 2017, Chen et al. 2018, Lim et al. 2018, Rampášek et al. 2019)、生物和基因学研究 (Riesselman et al. 2017, Grønbech et al. 2018, Eraslan et al. 2019)等. 深度学习在自然科学领域的成功应用对于发展先进结构材料的智能设计方法具有重要的借鉴价值.

5.2 基于机器学习的材料设计

如前文所述, 拓扑优化方法以优化设计为主, 通过寻找满足优化目标的最优解, 实现材料特定性能的最优化. 对于需要针对具体指定性能目标进行精准的材料设计问题, 基于"联结主义"的深度学习模型凭借其强大的数据拟合、特征提取性能以及处理高维度数据方面具有先天的优势, 在近几年受到超材料领域的高度关注. Tahersima等 (2018)提出了用于设计纳观光子设备的深度学习模型. 该模型一方面可以根据光子设备的孔洞排列方式快速预测该结构所对应的光谱传输响应(SPEC), 还可以进一步基于指定的光学响应反向设计与之对应的设备结构. Malkiel等 (2018)发展了用于光子晶体结构设计的深度学习模型, 可基于透射光谱预测光子晶体的纳观结构, 如图8 所示. Ma等 (2018)通过一个双向深度学习框架进行了手性超材料的研究. 该框架一方面可以正向预测超材料的光学性能, 同时还可以反向设计具有指定波长的三维手性超材料. Bessa等 (2019)基于贝叶斯模型在两个尺度下展开材料设计, 基于脆性聚合物制造出轻质、可恢复且具有超压缩性的超材料.

图8

图8   基于深度学习的光子晶体设计方法. (a)方法流程示意图, (b)用于正向预测投射光谱和反向设计光子晶体的深度学习模型示意 (Malkiel et al. 2018)


智能化材料设计一般关注设计目标与材料结构之间的隐藏关系. 在超材料设计中, 设计目标与材料拓扑结构往往需要通过高维度数据进行描述, 直接拟合出二者之间的逆向映射关系相对困难. 为此, 一些研究尝试通过监督学习与无监督学习的机器学习模型的组合与交互开展超材料设计. 这些方法一般利用生成模型(generative model)建立起潜在空间的力学、拓扑特征到高维度拓扑结构的对应关系, 再与确定判别模型(discriminative model)进一步结合, 实现材料的智能化设计. Qiu等 (2019)基于自动编码器和多层感知机深度学习模型拟合出电磁波吸收率与超表面拓扑矩阵之间的映射关系, 根据指定的设计目标(吸收率)直接计算出超表面拓扑结构. Liu等 (2018)基于生成对抗网络(GAN)发展了光学超表面的拓扑设计框架. 该框架首先预训练了成为"模拟器"的神经网络拟合出超表面拓扑结构与透射光谱的对应关系, 这个网络后续被用于光谱的快速计算. 有别于传统的GAN模型, 该框架基于生成器网络(generator)设计出超表面的拓扑和其透射光谱这两部分的误差构造损失函数, 用于更新生成器网络的参数. 经过训练的模型可基于指定投射光谱给出超表面拓扑构型设计方案. Ma等 (2019)发展了基于深度生成模型的光学超材料设计框架. 该框架采用了3个深度学习模型, 分别为识别模型、预测模型和生成模型. 识别模型将超材料拓扑结构及其光学响应编码到一个低维的潜在空间. 预测模型基于给定的超材料拓扑输出对光学响应. 生成模型则根据光学响应和潜在空间采样得到的低维度变量生成超材料拓扑设计方案.

5.3 基于机器学习的声学超材料设计

基于机器学习的声子晶体设计相关工作尚不多见. 作者所在的课题组在该领域进行了探索, 将基于图像的有限元建模、监督学习、无监督学习和强化学习等技术有机结合, 探索了机器学习在声学人工材料设计领域的应用. Li等 (2020)基于深度学习模型发展了声学人工材料的反向设计方法. 该方法的流程图如图9所示. 通过基于卷积神经网络结构的自动编码器提取声子晶体单胞的拓扑特征, 利用全连接的多层感知机建立起禁带与拓扑特征的内在关系. 该方法可基于指定的禁带位置和宽度设计出全新的声子晶体单胞结构. 此外, 该方法的核心框架还有望拓展用于反向设计具有指定功能的多种结构材料.

图9

图9   基于深度学习模型的声学人工材料设计方法流程图 (Li et al. 2020)


强化学习作为机器学习的一个分支, 其主要关注智能体如何与环境进行互动, 基于奖赏函数对模型进行动态更新, 从而不断逼近优化目标的全局最大值. 深度人工神经网络的引入进一步为传统强化学习模型注入了活力. 近年来, 深度强化学习在围棋 (Silver et al. 2017)、电子游戏 (Mnih et al. 2013, Arulkumaran et al. 2019)、自动驾驶 (Shalev-Shwartz et al. 2016, Sallab et al. 2017)、机器人控制 (Lillicrap et al. 2015)、自然语言处理 (Narasimhan et al. 2015)、机器视觉 (Caicedo & Lazebnik 2015)等诸多领域的成功应用再次点燃了人们探索通用人工智能的热情. 在自然科学领域, 深度强化学习技术也开始被用于新药物研发 (Popova et al. 2018)等. 强化学习方法也逐渐受到了材料设计领域的关注. Luo等 (2020)基于强化学习发展了一维声学人工材料的优化设计方法, 如图10所示. 该方法的核心思想是将优化设计目标转换为强化学习方法中的奖赏函数, 通过强化学习框架和有限元仿真环境的动态交互迭代地逼近奖赏函数的全局最优解, 可在一定约束条件下将一阶禁带宽度最大化, 还可用于反向设计具有指定禁带范围的一维声学人工材料的结构.

图10

图10   基于强化学习模型的一维声学人工材料设计方法流程图 (Luo et al. 2020)


5.4 基于机器学习的材料设计的现状与未来

随着深度学习与强化学习技术与材料、物理、力学学科的深入结合, 该类型智能设计方法已逐步应用于光子晶体、声子晶体等材料的设计. 基于深度学习的材料设计一般依靠大数据演绎出的微观结构与宏观等效性质之间的高维度的潜在映射关系. 这一类方法在样本集所覆盖的范围内可以保证较高的计算准确度. 然而, 当测试样本偏离训练集所包络的数据空间之外时, 深度学习模型的计算准确度会显著降低. 深度学习模型善于从高维欧式空间的数据学习出模式及关系. 也就是说, 深度学习模型中蕴含了从大量数据中萃取出的知识. 这些知识是通过抽象的神经网络结构所表示, 但这类知识的可解释性较差. 当前的大部分研究, 往往利用的是深度学习方法在处理大量复杂模拟、实验数据方面出色的拟合能力, 利用庞大的网络参数去描述传统符号函数难以表达的映射关系, 因此, 在材料及结构设计领域, 深度学习技术已经具备了出色的演绎能力. 近年来, 一些新的方法在对演绎结果的解释层面具有了一定的效果. 例如, 图是一种结构化数据, 它由一系列的对象(nodes)和关系类型(edges)组成. 传统的深度学习方法在处理这种非欧式空间的图数据上的表现并不尽如人意. 鉴于此, 研究人员借鉴了传统深度学习模型的思想, 设计出用于处理图数据的神经网络结构————图神经网络(graph neural networks, GNN) (Gori et al. 2005, Scarselli et al. 2008). 与传统神经网络模型相比, 图神经网络擅长推理, 具备很强的可解释性, 已在视觉推理、自然语言处理、可解释的推荐系统、新药物的发现、化合物筛选、疾病预测等许多领域取得了突破. 图网络的诞生和发展为实现更智能化的材料设计提供了新的思路和可能的工具, 为描述复杂数据关系所对应的内在物理性质或关系提供了可能.

然而, 正如上文提到的对于数据空间之外的关系难以描述等问题, 也反映了当前深度学习方法发展的困境与难点, 即如何让深度学习方法获得接近或远超人类的推理能力? 不难发现, 受限于机器学习算法理论, 一个深度学习模型能否在数据集之外继续保持良好的性能往往是后验的. 因此, 在使用该类型方法进行材料设计时, 应注意各类自变量均落在训练数据空间内部, 以保证模型使用的正确性. 同时, 也应时刻关注计算机科学领域对于深度学习算法的新发现与新成果, 找到能够与深刻的力学原理与材料设计思想结合的新方法.

强化学习算法则在一定程度上摆脱了数据集的限制, 基于强化学习的材料设计框架的核心思想是构建一个虚拟仿真环境, 在智能体与环境的动态交互过程中尝试逼近奖赏函数的全局最优, 最终实现设计的目标. 强化学习的顺利实施需要实时模拟仿真环境源源不断地提供训练数据, 仿真计算的效率直接影响了强化学习模型的训练效率. 然而, 非线性数值模拟仿真一般耗费大量的计算时间, 如何开发高效且泛化能力良好的数值仿真替代模型(surrogate model)或简化模型是未来该设计方法进一步普及的关键所在. 例如, 基于深度学习的替代模型已被应用于固体力学和流体力学的计算 (Lee et al. 2010, Jeon et al. 2019, Li et al. 2019). 这些替代模型的建立大多使用了端到端的训练数据, 往往针对于某个具体的仿真或应用场景, 且对其所能解决力学问题提出了较强的限制.

6 小结与展望

随着工程实践领域对材料性能需求逐渐趋向轻质化、高性能以及满足特定功能, 通过结构的精巧设计实现卓越力学性能的各类型先进结构材料势必成为未来材料研究的核心领域之一.

因此, 通用性的智能化设计方法是需要研究的核心问题. 结构材料的早期设计往往基于研究者的丰富经验, 或从天然材料中的元胞拓扑结构捕获灵感. 但是, 这类基于经验的设计方法往往难以给出全局最优的设计方案. 另外, 随着材料制备工艺和技术的发展, 对材料的设计方法提出了更高的要求. 拓扑优化方法被成功应用于元胞材料、光子晶体、声子晶体等材料的优化设计. 局限于现有拓扑优化方法以优化设计为主要目标, 该方法在如何基于指定的力学指标实现精准的反向设计方面尚存挑战. 此外, 受限于自身算法的局限性, 拓扑优化在动态问题设计目标和非线性问题优化函数的给定等问题上, 仍未有较好的解决方案. 如何智能、自动地进行材料设计将是未来材料设计领域的新需求.

近年来, 基于深度学习和强化学习的人工智能技术在围棋、电子游戏、自动驾驶、机器人控制、自然语言处理、机器视觉等诸多计算机科学领域得到了成功应用. 同时, 这些技术开始在药物分子结构、生物和基因学研究等自然科学领域的大放异彩, 让人们再次看到人工智能的广阔应用前景, 为先进结构材料的智能设计提供了可借鉴的思路.

科技的进步对未来的材料性能提出了更高要求. 设计并制造具备自适应性、多功能性和可调性的先进结构材料将成为材料学的发展新方向. 仅仅凭借传统材料设计方法可能已经无法满足这些全新的设计需求. 目前, 智能化材料设计的相关研究目前还处于相对起步阶段, 但已逐渐呈现出蓬勃的发展势头. 有理由期待该领域的研究者将材料学、力学、数据科学进行更广泛和深入的结合, 发展出更加智能、高效的材料设计方法.

致谢

国家自然科学基金资助项目 (11722218, 11972205).

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