Scalable Dielectric Tensor Predictions for Inorganic Materials using Equivariant Graph Neural Networks

TL;DR

The paper addresses the high cost of predicting dielectric tensors for inorganic materials by introducing GoeCTP, a frame-averaging, $O(3)$-equivariant framework that decouples symmetry enforcement from backbone design. By using frame averaging, GoeCTP supports flexible, non-equivariant message passing while preserving the correct tensor transformation properties, enabling scalable architectures and effective pretraining/fine-tuning strategies. Across JARVIS-DFT and Materials Project datasets, GoeCTP variants achieve state-of-the-art or competitive accuracy, and large-scale virtual screening identifies novel high-dielectric and highly anisotropic materials (e.g., Ba$_2$SmTaO$_6$, Zr(InBr$_3$)$_2$, SeI$_2$). The work demonstrates practical potential for rapid dielectric-material discovery, offering improved flexibility over prior PFP-reliant approaches and enabling broader elemental coverage and scalable screening pipelines.

Abstract

Accurate prediction of dielectric tensors is essential for accelerating the discovery of next-generation inorganic dielectric materials. Existing machine learning approaches, such as equivariant graph neural networks, typically rely on specially-designed network architectures to enforce O(3) equivariance. However, to preserve equivariance, these specially-designed models restrict the update of equivariant features during message passing to linear transformations or gated equivariant nonlinearities. The inability to implicitly characterize more complex nonlinear structures may reduce the predictive accuracy of the model. In this study, we introduce a frame-averaging-based approach to achieve equivariant dielectric tensor prediction. We propose GoeCTP, an O(3)-equivariant framework that predicts dielectric tensors without imposing any structural restrictions on the backbone network. We benchmark its performance against several state-of-the-art models and further employ it for large-scale virtual screening of thermodynamically stable materials from the Materials Project database. GoeCTP successfully identifies various promising candidates, such as Zr(InBr$_3$)$_2$ (band gap $E_g = 2.41$ eV, dielectric constant $\overline{\varepsilon} = 194.72$) and SeI$_2$ (anisotropy ratio $α_r = 96.763$), demonstrating its accuracy and efficiency in accelerating the discovery of advanced inorganic dielectric materials.

Figures (6)

• Figure 1: (a) Illustration of GoeCTP. Given an input crystal, GoeCTP first applies frame averaging to align the crystal structure to its canonical orientation. A crystal graph is then constructed, and the message passing layers together with the readout module generate a predicted dielectric tensor $\boldsymbol{\varepsilon}$ corresponding to this canonical orientation. The frame $\text{F}_1$ computed at the input stage is subsequently applied to this canonical tensor to obtain the final tensor prediction. When an arbitrary rotation or reflection $\text{R}$ is applied to the input crystal structure, frame averaging again aligns the transformed crystal to the same canonical orientation. In this case, the resulting frame satisfies $\text{F}_2=\text{R}\text{F}_1$. Consequently, at the output stage, the predicted tensor is transformed consistently, ensuring that the final output satisfies the required O(3) equivariance. (b) Diagram of the GoeCTP pretraining strategy. During pretraining on a scalar property dataset, the frame obtained through frame averaging is not applied to the output. After pretraining is completed, the readout module is replaced, and the message passing layers are initialized with the pretrained weights. The model is then fine-tuned on the tensor dataset.
• Figure 2: Impact of message passing depth on network performance. For each crystal system, the mean absolute error is reported (points), and the shaded regions denote standard deviations across multiple runs, enabling comparison among GoeCTP, GoeCTP (Mat.), and GoeCTP (iCom.).
• Figure 3: Comparison of model performance between training from scratch and fine tuning. Training from scratch indicates that the models are trained solely on the tensor datasets, while fine tuning corresponds to first pretraining GoeCTP on a large scalar dataset followed by fine tuning on the tensor datasets.
• Figure 4: Performance of GoeCTP models on the test split of the Materials Project dataset for two prediction tasks. Panels (a), (b), and (c) show the results of GoeCTP, GoeCTP (Mat.), and GoeCTP (iCom.) respectively on the polycrystalline dielectric constant prediction task. Panels (d), (e), and (f) present the corresponding results of GoeCTP, GoeCTP (Mat.), and GoeCTP (iCom.) on the tensor eigenvalue prediction task.
• Figure 5: Benchmarking our approach against other algorithms on the Matbench dataset.