Brandao Eduardo, Colombier Jean-Philippe, Duffner Stefan, Emonet Rémi, Garrelie Florence, Habrard Amaury, Jacquenet François, Nakhoul Anthony, Sebban Marc
Laboratoire Hubert Curien UMR5516, UJM-Saint-Etienne, CNRS, IOGS, Université de Lyon, F-42023 St-Etienne, France.
CNRS, INSA-Lyon, LIRIS, UMR5205, Université de Lyon, F-69621 Villeurbanne, France.
Entropy (Basel). 2022 Aug 9;24(8):1096. doi: 10.3390/e24081096.
A self-organization hydrodynamic process has recently been proposed to partially explain the formation of femtosecond laser-induced nanopatterns on Nickel, which have important applications in optics, microbiology, medicine, etc. Exploring laser pattern space is difficult, however, which simultaneously (i) motivates using machine learning (ML) to search for novel patterns and (ii) hinders it, because of the few data available from costly and time-consuming experiments. In this paper, we use ML to predict novel patterns by integrating partial physical knowledge in the form of the Swift-Hohenberg (SH) partial differential equation (PDE). To do so, we propose a framework to learn with few data, in the absence of initial conditions, by benefiting from background knowledge in the form of a PDE solver. We show that in the case of a self-organization process, a feature mapping exists in which initial conditions can safely be ignored and patterns can be described in terms of PDE parameters alone, which drastically simplifies the problem. In order to apply this framework, we develop a second-order pseudospectral solver of the SH equation which offers a good compromise between accuracy and speed. Our method allows us to predict new nanopatterns in good agreement with experimental data. Moreover, we show that pattern features are related, which imposes constraints on novel pattern design, and suggest an efficient procedure of acquiring experimental data iteratively to improve the generalization of the learned model. It also allows us to identify the limitations of the SH equation as a partial model and suggests an improvement to the physical model itself.
最近提出了一种自组织流体动力学过程,以部分解释镍上飞秒激光诱导纳米图案的形成,这些图案在光学、微生物学、医学等领域具有重要应用。然而,探索激光图案空间很困难,这同时(i)促使使用机器学习(ML)来寻找新颖图案,(ii)又阻碍了它,因为昂贵且耗时的实验可获得的数据很少。在本文中,我们通过以Swift-Hohenberg(SH)偏微分方程(PDE)的形式整合部分物理知识,使用ML来预测新颖图案。为此,我们提出了一个框架,通过受益于PDE求解器形式的背景知识,在没有初始条件的情况下用少量数据进行学习。我们表明,在自组织过程的情况下,存在一种特征映射,其中初始条件可以安全地忽略,图案可以仅根据PDE参数来描述,这极大地简化了问题。为了应用这个框架,我们开发了SH方程的二阶伪谱求解器,它在精度和速度之间提供了很好的折衷。我们的方法使我们能够预测与实验数据高度一致的新纳米图案。此外,我们表明图案特征是相关的,这对新颖图案设计施加了约束,并提出了一种迭代获取实验数据以提高学习模型泛化能力的有效程序。它还使我们能够识别SH方程作为部分模型的局限性,并建议对物理模型本身进行改进。