Deep learning statistical defect models on magnetic material dynamic and static properties

TL;DR

A convolutional neural network and a physics-informed neural network combined with theory of functional connections are developed to predict the dispersion relation given defect parameters and physical constraints to achieve statistical predictions measured in physical units.

Abstract

The modeling of realistic magnetic materials requires the inclusion of defects. Based on the pseudospectral Landau-Lifshitz description of magnetisation dynamics, we propose a statistical model that takes into account defects, specifically vacancies. This statistical model can be integrated with deep learning techniques that correlate defect thresholds with relevant physical observables. We develop a convolutional neural network and a physics-informed neural network combined with theory of functional connections to predict the dispersion relation given defect parameters and physical constraints. A two-branch convolutional neural network is developed to predict domain-wall widths depending on defects threshold, taking into account the spatial profile and domain-wall width separately to achieve a prediction. The proposed physics-informed approaches leverage deep-learning and achieve statistical predictions measured in physical units. This is a stepping stone towards the discovery of new materials and the determination of minimal defect thresholds required for desired dynamics, states, or topological textures.

Figures (6)

• Figure 1: Modeling of a defective material.a A 1D-chain of atoms can have vacancies at random locations, illustrated by red circles. This chain is represented by a digital signal where 1 indicates atoms and 0 represents vacancies. $\sigma$ represents the average length of defect-free atomic chain and $\tau$ represents the average length of vacancies. b The Fourier transform of the RTN signal, Eq. \ref{['eq:machlup']}, shown as a function of $k$ and $\tau$ for $\sigma=10$ nm. When $\tau=0$, $S(k) = \delta(k)$. As $\tau$ increases, the broadband Lorentzian spectrum grows in amplitude. c Dispersion relation calculated for an ideal material and d a material in which $\sigma=10$ nm and $\tau=5$ nm. In both panels, the ideal magnon dispersion relation of Eq. \ref{['eq:omega']} scaled by $\gamma\mu_0M_s$ is shown by a red dashed curve. The color scheme is found in Ref. colorscheme. e Domain wall profile for an ideal material, blue curve $\tau=0$, and a defective material, red curve $\sigma=10$ nm and $\tau=5$ nm. f Surface plot of the the domain-wall width as a function of $\sigma$ and $\tau$, calculated from numerically relaxed domain walls.
• Figure 2: Neural network architecture for TFC dispersion prediction. The dispersion relation and $\sigma$ and $\tau$ pairs are given as inputs to a CNN for feature extraction and efficient pooling, with normalization in between each layer. The output is passed to the coefficient predictor that learns based on specific physical parameter constraints and finally a new dispersion is constructed preserving the original structure by the TFC.
• Figure 3: Dispersion relation predictions from the TCF-PINN learned function. Dispersion relations computed by the SPS-LL for a$\sigma = 22.9$ nm, $\tau=3.0$ nm, and $X=3.65$ THz and b$\sigma=15.1$ nm, $\tau=12.4$ nm, and $X=2.45$ THz. The predicted dispersion relation from the given $\sigma$ and $\tau$ are plotted by dashed magenta curves, in good agreement with the numerical solution. The ideal dispersion relation is shown by dotted red curves for reference. The color scheme is found in Ref. colorscheme. c Training loss trend for the TCF-PINN learned function. This training loss plot shows an optimal learning trend.
• Figure 4: Architecture to predict domain-wall widths. The CNN takes the magnetization profile and associated domain wall width calculated with the defect noise parameters and returns the defect parameters for that width.
• Figure 5: Learned domain-wall widths as a function of $\sigma$ and $\tau$. a Actual (blue symbols) and predicted (red symbols) widths as a function of defect density T (nm). The learned domain-wall widths closely follow the trend expected from numerical calculations. b Histogram of the domain-wall width errors. The mean of the distribution is 0.077 nm and the standard deviation is $0.835$ nm. c Training loss trend for the CNN learned width. For the training we used large batch training in increments of 25 epochs.