Simulating the mechanical response of advanced materials can be done more
accurately using concurrent multiscale models than with single-scale
simulations. However, the computational costs stand in the way of the practical
application of this approach. The costs originate from microscale Finite
Element (FE) models that must be solved at every macroscopic integration point.
A plethora of surrogate modeling strategies attempt to alleviate this cost by
learning to predict macroscopic stresses from macroscopic strains, completely
replacing the microscale models. In this work, we introduce an alternative
surrogate modeling strategy that allows for keeping the multiscale nature of
the problem, allowing it to be used interchangeably with an FE solver for any
time step. Our surrogate provides all microscopic quantities, which are then
homogenized to obtain macroscopic quantities of interest. We achieve this for
an elasto-plastic material by predicting full-field microscopic strains using a
graph neural network (GNN) while retaining the microscopic constitutive
material model to obtain the stresses. This hybrid data-physics graph-based
approach avoids the high dimensionality originating from predicting full-field
responses while allowing non-locality to arise. By training the GNN on a
variety of meshes, it learns to generalize to unseen meshes, allowing a single
model to be used for a range of microstructures. The embedded microscopic
constitutive model in the GNN implicitly tracks history-dependent variables and
leads to improved accuracy. We demonstrate for several challenging scenarios
that the surrogate can predict complex macroscopic stress-strain paths. As the
computation time of our method scales favorably with the number of elements in
the microstructure compared to the FE method, our method can significantly
accelerate FE2 simulations.

利用并行多尺度模型比单尺度模拟可以更准确地模拟先进材料的力学响应，但是计算成本是该方法实际应用的障碍。本研究提出了一种备选的代理建模策略，允许保持问题的多尺度特性，并可与有限元求解器交替使用。通过使用图神经网络 (GNN) 预测完全场微观应变，并保留微观本构材料模型以获得应力，我们在弹塑性材料上实现了这一点。这种基于数据和物理的图形方法避免了预测完全场响应所产生的高维度，并允许非局部性产生。通过对各种网格进行训练，GNN 学习了对未见过的网格的泛化，使单个模型可以用于一系列的微结构。GNN 中嵌入的微观本构模型隐式地跟踪历史依赖变量，并提高了准确性。我们证明了对于几个具有挑战性的情景，代理模型能够预测复杂的宏观应力 - 应变路径。由于我们的方法的计算时间与微结构中的元素数量相比的呈良好的缩放规律，因此我们的方法可以显著加速 FE2 模拟。

基于微观结构的图神经网络用于加速多尺度模拟

A Microstructure-based Graph Neural Network for Accelerating Multiscale  Simulations

Advanced materials are needed to further next-generation technologies such as
quantum computing, carbon capture, and low-cost medical imaging. However,
advanced materials discovery is confounded by two fundamental challenges: the
challenge of a high-dimensional, complex materials search space and the
challenge of combining knowledge, i.e., data fusion across instruments and
labs. To overcome the first challenge, researchers employ knowledge of the
underlying material synthesis-structure-property relationship, as a material's
structure is often predictive of its functional property and vice versa. For
example, optimal materials often occur along composition-phase boundaries or
within specific phase regions. Additionally, knowledge of the
synthesis-structure-property relationship is fundamental to understanding
underlying physical mechanisms. However, quantifying the
synthesis-structure-property relationship requires overcoming the second
challenge. Researchers must merge knowledge gathered across instruments,
measurement modalities, and even laboratories. We present the
Synthesis-structure-property relAtionship coreGionalized lEarner (SAGE)
algorithm. A fully Bayesian algorithm that uses multimodal coregionalization to
merge knowledge across data sources to learn synthesis-structure-property
relationships.

应用贝叶斯算法的 SAGE 算法通过多模态核主成分分析将来自不同数据源的知识合并，学习合成 - 结构 - 性能关系，从而克服高维复杂材料搜索空间和知识融合的挑战。

通过数据融合学习材料的结构 - 性能关系：贝叶斯共区相关 N 维分段函数学习

Learning material synthesis-structure-property relationship by data  fusion: Bayesian Co-regionalization N-Dimensional Piecewise Function Learning

The rapid design of advanced materials is a topic of great scientific
interest. The conventional, ``forward'' paradigm of materials design involves
evaluating multiple candidates to determine the best candidate that matches the
target properties. However, recent advances in the field of deep learning have
given rise to the possibility of an ``inverse'' design paradigm for advanced
materials, wherein a model provided with the target properties is able to find
the best candidate. Being a relatively new concept, there remains a need to
systematically evaluate how these two paradigms perform in practical
applications. Therefore, the objective of this study is to directly,
quantitatively compare the forward and inverse design modeling paradigms. We do
so by considering two case studies of refractory high-entropy alloy design with
different objectives and constraints and comparing the inverse design method to
other forward schemes like localized forward search, high throughput screening,
and multi objective optimization.

通过两个高熵合金设计案例研究，直接、定量地比较正向和逆向设计模型范式，并将逆向设计方法与局部前向搜索、高通量筛选和多目标优化等其他前向方案进行对比。