<p>We present an interpretable machine learning model to predict accurately the complex rippling deformations of multiwalled carbon nanotubes (MWCNTs) made of millions of atoms.&nbsp; Walls of MWCNTs are crystalline membranes having very low bending modulus and very high in-plane modulus. Besides, the inter-wall van der Waals interactions keep them separated and guide the deformation. Under loading, the walls bend to minimize their inplane strain following a near isometric deformation, leading to rippling patterns. Accurate and efficient simulation tools to predict the complex deformations of large MWCNTs are needed but still elusive. Atomistic-physics-based models are accurate but computationally prohibitive for such large systems. Whereas, existing continuum models, which consider them as thin shells and beams ignore the underlying atomistic physics. Towards this, Atomistic--Continuum (AC) models have been developed by integrating atomistic and continuum frameworks. State-of-the-art AC models are very efficient but still require high-performance computing efforts for large MWCNTs, which is the bottleneck for the exploration of the physics of these materials. Machine Learning (ML) methods, such as deep neural networks (DNNs) are intensely investigated for accelerating mechanics, physics, and materials research, however, so far most of the applications are limited to the prediction of low-dimensional properties, such as material moduli. On the contrary, discretized material deformation requires prediction in a high-dimensional space. Deep learning models can predict low-dimensional (e.g., convolutional neural networks autoencoder) or high-dimensional outputs (e.g., encoder-decoder). However, these deep learning models require high-dimensional inputs. State-of-the-art DNNs cannot accurately predict high-dimensional targets from a few input features. The objective of the present paper is to create a machine learning model to accurately and efficiently predict high-dimensional discretized deformations of MWCNTs as output from low-dimensional inputs. In this work, we have developed a machine learning model that comprises a novel dimensionality reduction technique and a deep neural network-based learning in the reduced dimension. The proposed nonlinear dimensionality reduction technique extends the functional principal component analysis to satisfy the geometric constraint of MWCNT. Its novelty lies in designing a function space that satisfies the constraint exactly, which is crucial for efficient dimensionality reduction. Owing to the dimensionality reduction and several other strategies adopted in the present paper, learning through deep neural networks is remarkably accurate. The model extracts universally dominant patterns of deformation in an unsupervised manner. These patterns are comprehensible and explain how the model predicts, yielding interpretability. The proposed model can form a basis for an exploration of machine learning toward the mechanics of one- and two-dimensional materials.</p>

Interpretable Machine Learning Model for the Deformation of Multiwalled Carbon Nanotubes Under Torsion and Bending

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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