材料科学中的分层基于物理的机器学习：蜘蛛丝案例研究
Hierarchical physically based machine learning in material science: the case study of spider silk
AI总结：
本文提出利用Pareto front识别变量层级并推导因果关系的基于物理的多尺度机器学习框架，并以蜘蛛丝验证其相较传统数据驱动建模的优势。
摘要：
多尺度现象表现出复杂的结构-功能关系，预测其宏观行为需要推导不同尺度上的微分方程。这些方程的复杂性以及必要参数的数量使开发有效的预测模型具有挑战性。为克服这一点，研究人员探索利用来自人工智能和机器学习的先进数值技术。在此，我们聚焦多尺度现象中的一个基本方面，即识别变量的分层作用。通过采用Pareto front（帕累托前沿）解释，我们旨在从实验性多尺度分析出发，推导用于材料建模的简单而准确的关系。从物理角度看，目标是从较低尺度的数据推导较高尺度的信息，并尽可能遵循其分层顺序。所提方法的一个关键方面是推导不同变量之间的因果关系，以便与现有理论概念以及数据建模可能产生的新解释进行比较。这形成了一个逐步近似过程：从数据建模到理论方程，再回到数据建模。为证明我们的多尺度数值方法相较于经典的、非基于物理的数据建模技术的关键优势，我们考虑蜘蛛丝这一具体示例，该材料以其卓越性能和生物启发潜力而闻名。事实上，它表现出由分子尺度上氨基酸聚集形成的介观结构所导致的复杂行为。我们认为，由于研究结果具有通用性，我们的方法可能在许多由多尺度、分层微分方程调控所观察现象的领域中成为概念验证。
英文摘要：
Multiscale phenomena exhibit complex structure-function relationships, and predicting their macroscopic behavior requires deducing differential equations at different scales. The complexity of these equations and the number of essential parameters make developing effective, predictive models challenging. To overcome this, researchers explore leveraging advanced numerical techniques from artificial intelligence and machine learning. Here, we focus on a fundamental aspect in multiscale phenomena, i.e the recognition of the hierarchical role of variables. By adopting a Pareto front interpretation, we aim to deduce simple and accurate relations for material modeling, starting from experimental multiscale analyses. From a physical point of view, the aim is to deduce information at higher scales from lower scales data, possibly respecting their hierarchical order. A crucial aspect of the proposed approach is the deduction of causality relations among the different variables to be compared with the available theoretical notions and possibly new interpretations resulting by the data modelling. This result in a stepwise approximation going from data modelling to theoretical equations and back to data modelling. To demonstrate the key advantages of our multiscale numerical approach, compared to classical, non-physically based data modelling techniques, we consider the explicit example of spider silk, known for its exceptional properties and bioinspiration potential. Indeed, it presents a complex behavior resulting from mesostructures formed by the aggregation of amino acids at the molecular scale. We argue that, due to the generality of our results, our approach may represent a proof of concept in many fields where multiscale, hierarchical differential equations regulate the observed phenomenon.
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