Dielectric Tensor Prediction for Inorganic Materials Using Latent Information from Preferred Potential

TL;DR

This work addresses the scarcity and tensorial nature of dielectric data by introducing DTNet, an equivariant neural network that leverages a frozen PreFerred Potential (PFP) encoder to predict electronic, ionic, and total dielectric tensors across 72 elements. By preserving $O(3)$ equivariance through a specialized readout, DTNet achieves state-of-the-art accuracy on MP/MatBench dielectric tasks and demonstrates data-efficient transfer learning for tensorial properties. The authors validate the approach with virtual screening on over 14k stable materials, identifying high-$\varepsilon$ and highly anisotropic candidates (e.g., Cs2Ti(WO4)3, CsZrCuSe3) and performing 35 DFPT calculations to confirm predictions. Collectively, the method accelerates tensorial property discovery and illustrates that higher-order latent features from pretrained energy models can improve predictions for diverse tensor orders with limited labeled data.

Abstract

Dielectrics are crucial for technologies like flash memory, CPUs, photovoltaics, and capacitors, but public data on these materials are scarce, restricting research and development. Existing machine learning models have focused on predicting scalar polycrystalline dielectric constants, neglecting the directional nature of dielectric tensors essential for material design. This study leverages multi-rank equivariant structural embeddings from a universal neural network potential to enhance predictions of dielectric tensors. We develop an equivariant readout decoder to predict total, electronic, and ionic dielectric tensors while preserving O(3) equivariance, and benchmark its performance against state-of-the-art algorithms. Virtual screening of thermodynamically stable materials from Materials Project for two discovery tasks, high-dielectric and highly anisotropic materials, identifies promising candidates including Cs2Ti(WO4)3 (band gap $E_g=2.93 \mathrm{eV}$, dielectric constant $\varepsilon=180.90$) and CsZrCuSe3 (anisotropic ratio $α_r = 121.89$). The results demonstrate our model's accuracy in predicting dielectric tensors and its potential for discovering novel dielectric materials.

Figures (9)

• Figure 1: Diagram of the equivariant model for dielectric tensor prediction. The input graph is represented by initialized atom attributes $\mathcal{V}=\{(\boldsymbol{a}_s, \boldsymbol{a}_v, \boldsymbol{a}_t)_i\}_{i=1:N^a}^0$ and bond attributes $\mathcal{E}=\{(\boldsymbol{b}_{s,{\{i,j\}}}, \boldsymbol{b}_{v,{\{i,j\}}})_k\}_{k=1:N^b}^0$ between atoms with indices of $i$ and $j$, where $N^a$ and $N^b$ are number of atoms and bonds. The intermediate knowledge output $\{(\boldsymbol{a}_s, \boldsymbol{a}_v, \boldsymbol{a}_t)_i\}_{i=1:N^a}^n$ and $\{(\boldsymbol{b}_{s,{\{i,j\}}}, \boldsymbol{b}_{v,{\{i,j\}}})_k\}_{k=1:N^b}^n$ from the $n$-th layer GCN of PFP is fed into an equivariant readout block to perform message interactions among different rank representations for a downstream task, i.e., dielectric tensor prediction here.
• Figure 2: Schematic architecture of the equivariant dielectric model DTNet. (a) Overview of the DTNet framework; (b) Implementation of an equivariant block in DTNet; (c) Implementation of the readout block for dielectric tensor output
• Figure 3: Rotational equivariance on dielectric constants of inorganic materials. $\overrightarrow{E}$ is the external electric field, $\overrightarrow{D}$ is the corresponding electric displacement, and $\boldsymbol{\varepsilon}$ is the $3\times3$ dielectric tensor.
• Figure 4: (a) $\varepsilon^\infty-\varepsilon^0$ map of structures in the dataset, colored by $\varepsilon$; (b)Counts of crystal system types in teh dataset; (c) Element counts for atoms in the structures with available dielectric properties on Materials Project. Elements under blue are not supported by PFP. Elements under white are supported by PFP but do not appear in the dataset.
• Figure 5: Performance of DTNet models on dielectric data from Materials Project. (a-b) Plot of the mean error/correlation (points) with standard deviation (shadow) for 5 runs against the intermediate embedding generated from the PFP-Ln as DTNet inputs, showing both transfer learning results and training from scratch results for comparison. (c-e) Multiple MAE metrics in the dielectric tensor for different crystal systems on the prediction of the electronic, ionic and total task.