A cyclical route linking fundamental mechanism and AI algorithm: An example from tuning Poisson's ratio in amorphous networks

TL;DR

The investigation into the relationship between extreme Poisson's ratio values and the structure of amorphous networks is used as a case study to illustrate how machine learning methods can assist in revealing underlying physical mechanisms.

Abstract

"AI for science" is widely recognized as a future trend in the development of scientific research. Currently, although machine learning algorithms have played a crucial role in scientific research with numerous successful cases, relatively few instances exist where AI assists researchers in uncovering the underlying physical mechanisms behind a certain phenomenon and subsequently using that mechanism to improve machine learning algorithms' efficiency. This article uses the investigation into the relationship between extreme Poisson's ratio values and the structure of amorphous networks as a case study to illustrate how machine learning methods can assist in revealing underlying physical mechanisms. Upon recognizing that the Poisson's ratio relies on the low-frequency vibrational modes of dynamical matrix, we can then employ a convolutional neural network, trained on the dynamical matrix instead of traditional image recognition, to predict the Poisson's ratio of amorphous networks with a much higher efficiency. Through this example, we aim to showcase the role that artificial intelligence can play in revealing fundamental physical mechanisms, which subsequently improves the machine learning algorithms significantly.

Figures (5)

• Figure 1: Tuning $\nu$ from positive to negative in three types of amorphous networks. a, a schematics showing the positive and negative $\nu$ behaviors. The red arrows indicate the uniaxial stretching, the original state is drawn in blue, and the deformed state is drawn in light gray. For $\nu>0$, the longitudinal direction elongates while the transverse direction shrinks; for $\nu<0$, both directions elongates. b-d, the construction of three types of amorphous networks: the distorted triangular lattice, the Delaunay-triangulated random network, and the packing-derived network. e, a schematics demonstrating local minimum and global minimum. f-h, tuning towards either positive or negative Poisson's ratio from the same initial state, for the three types of amorphous networks shown on the left. Note that all configurations throughout tuning contain only convex polygons. i, the statistics of single-bond length changes under stretching. Each data point represents one single bond: its x and y coordinates are the length changes under x and y stretching respectively. The middle panel is the original system, and the top and bottom panels are the systems after $\nu$-increase and $\nu$-decrease tunings respectively. Clearly, systems with positive $\nu$ and negative $\nu$ exhibit distinct data distributions: the former are mostly in quadrants II and IV while the latter are mostly in quadrants I and III. j, the variance of data points similar to i is plotted against $\nu$, and a reasonable collapse is observed.
• Figure 2: The classical auxetic structures are fundamentally different from the auxetic structures discovered by our machine learning. a-c,the three classical structures, characterized by $\nu<0$, $\nu>0$, and $\nu \approx 0$, are derived from the fundamental bow-tie structure. d-l, the three rows correspond to the three different amorphous systems. Within each row, the middle panel shows the original structure, and the left and right panels show the negative and more positive configurations found by the machine learning. Apparently, in the left panels of auxetic structures there is no concave structures typically existing in the classical auxetic structures. Also note that the negative-$\nu$ panels on the left are structurally very similar to the positive-$\nu$ panels on the right with almost a same $z$.
• Figure 3: Experimental realization with 3D-printing. a, experimental setup for $\nu$ measurement. The sample is under a compression loading on its top surface driven by two step motors. Compression strain and speed are precisely controlled by the motors. The Poisson’s ratio is measured from the area change of sample during the compression, which is recorded by a camera in front of the sample. b-j, the three rows show the situations of the three amorphous systems. Each snapshot is taken at the compression strain of $\varepsilon = -0.1$, and the red boxes indicate the original boundary without loading. Clearly, the left panels exhibit a negative $\nu$, the middle panels exhibit a nearly-zero $\nu$, and the right panels exhibit a positive $\nu$. (Multimedia view).
• Figure 4: The effective Poisson's ratio of normal modes, $\nu'$, determines the actual $\nu$ of the system. a, the left panel shows the normal mode at the frequency $\omega^+$, and the gray area indicates the original state. The right panel shows the configuration after adding the vibrational vectors: clearly the network expands in y direction and shrinks in x direction, which is a typical feature of positive Poisson's ratio. b, The normal mode at the frequency $\omega^-$ shows simultaneous expansion in both x and y directions, which is a typical auxetic behavior. c, $|C_{\omega i}|^2$ shows the weight or importance of different normal modes in an actual stretching deformation. Only the low-frequency range is important and the values at high frequencies are all zero. Clearly there are two peaks in the inset: one at $\omega^+$ with positive $\nu'$ and one at $\omega^-$ with negative $\nu'$. The superposition of the two $\nu'$ based on their weights, $\overline{\nu'}=|C_{\omega+}|^2 \nu'(\omega^+) + |C_{\omega-}|^2 \nu'(\omega^-)$, determines the actual $\nu$. d, $\overline{\nu'}$ from normal modes versus actual $\nu$ shows a nice linear relation, and an excellent data collapse across various systems is observed. Clearly, one to two normal modes can universally determine the actual Poisson's ratio across various amorphous systems. e, from top to bottom, as $\nu$ is tuned to negative values, the weight of $\omega^-$ keeps increasing to dominant while the weight of $\omega^+$ keeps decreasing to negligible. When the two modes have similar weights, their $\nu'$ cancels out and the system exhibits a nearly-zero $\nu$ (see the middle panel). The positions of two peaks first approach each other, then overlap and eventually separate apart. f, from top to bottom, as $\nu$ is tuned to more positive values, the weight of $\omega^+$ keeps increasing to dominant while the weight of $\omega^-$ keeps decreasing to negligible. The two peak positions keep separating apart.
• Figure 5: Scientific discovery serves as a catalyst for advancements in deep learning. a, The presence of bond-crossing areas poses challenges for deep learning models, as neural networks struggle to discern whether two crossed bonds share a common node. This challenge is mitigated by substituting images with the dynamical matrix as input, as illustrated by the architecture of AlexNet. b, Comparisons of the training results of CNN models using images and dynamical matrices as inputs. c, Comparing the prediction performance of Poisson's ratio from training based on dynamical matrix and images as the testing dataset, which demonstrates a much better performance from training based on dynamic matrix. d, Calculation of time cost by directly solving equilibrium equations and CNN models based on images and dynamical matrices. The comparison is conducted across amorphous networks of different sizes, ranging from $12 \times 12$ to $32 \times 32$.