Equivariant Graph Neural Networks Improve Optical Spectra Prediction for Materials Screening

Abstract: Scalable prediction of optical spectra is a critical component of high-throughput materials screening for optoelectronic applications such as solar cells. Existing surrogate models are trained on spectra computed from lower levels of theory or rely on rotation-invariant scalar features, limiting their geometric expressiveness. We explore the use of equivariant graph neural networks for optical spectra prediction, adapting GotenNet to this task and evaluating it on multiple datasets including a recently published collection of 10,533 structures with spectra computed at the level of the random phase approximation (RPA). The proposed model outperforms the current state of the art, with the largest gains in the 0-8 eV range and on predicting the static real permittivity, both of particular relevance for thin-film optics.

• The paper demonstrates that 3D equivariant GNNs significantly improve optical spectra prediction accuracy, especially in the 0–8 eV range.
• It introduces GotenNetOpt with advanced feature embeddings like covalent radius and distance-based graph construction tailored for RPA-computed spectra.
• Empirical results reveal up to 63% error reduction and enhanced screening viability for optoelectronic materials using ML surrogates.

Equivariant Graph Neural Networks for Optical Spectra Prediction

Motivation and Context

High-throughput screening of materials for optoelectronic applications such as photovoltaics critically depends on efficient and accurate prediction of optical spectra. Traditional approaches based on experimental measurement or ab initio simulations (DFT, MBPT) are prohibitively resource-intensive, especially for large-scale computational exploration. The main paradigm for scalable property prediction leverages ML surrogates trained on high-fidelity spectral databases. State-of-the-art models such as OptiMate3B encode structural features via rotation-invariant scalars, sometimes supplementing with explicit angular information through graph constructions such as Voronoi-based line graphs, which restrict connectivity and increase architectural complexity.

The present work ("Equivariant Graph Neural Networks Improve Optical Spectra Prediction for Materials Screening" (2606.19133)) investigates the use of 3D equivariant GNNs for optical spectra prediction and adapts GotenNet, a recent SO(3)-equivariant GNN, for this purpose. The study includes extensive benchmarking on both IPA- and RPA-computed spectra, notably leveraging a large, high-quality RPA dataset of 10,533 materials, and demonstrates substantial improvements in prediction fidelity—particularly in the spectroscopically relevant 0–8 eV range and for static real permittivity.

Technical Approach and Architectural Developments

Equivariant GNNs and Geometric Inductive Bias

The architectural centerpiece is GotenNetOpt, derived from GotenNet. Equivariant GNNs propagate tensorial features that consistently transform under symmetry group actions, specifically SO(3) for rotations. This guarantees geometric consistency and efficient capture of directional and angular correlations, which scalar-invariant architectures either lack or encode explicitly through auxiliary graph constructs. The message-passing layers update steerable node and edge representations via degree-$l$ spherical harmonics, with $l=1$ capturing vectorial information and higher $l$ encoding complex angular correlations.

Embedding and Feature Design

Key architectural modifications include:

• Covalent Radius Embeddings: Inspired by prior work (GNNOpt), covalent radii are encoded via Gaussian RBFs and integrated multiplicatively to modulate atomic species embeddings. This physically-informed feature enhances discriminability for chemically similar atoms with distinct bond radii.
• Distance-Based Graph Construction: Edges are defined by a 6 Å cutoff, yielding more physically meaningful graphs compared to Voronoi-based constructions used in OptiMate3B. Periodic boundary conditions are applied for unit cell representation.
• Readout Layer: The architecture employs an attention-weighted global pooling readout followed by a deep MLP, mirroring OptiMate3B for direct comparability.

Training and Evaluation Protocols

Models are pre-trained on IPA spectra and fine-tuned on RPA, reflecting the greater physical accuracy and many-body fidelity of RPA calculations. Evaluation metrics include mean absolute error (MAE), mean squared error (MSE), and similarity coefficient (SC) over frequency ranges, with particular emphasis on the physically relevant 0–8 eV sub-spectrum. Additional analysis focuses on static real permittivity prediction and per-element accuracy as a function of training frequency.

Empirical Results

Quantitative Performance

GotenNetOpt consistently outperforms OptiMate3B across all datasets and spectral components. Notable results:

• Full-range (0–20 eV) median MAE/MSE improvements (RPA): 18–32%, with largest gains for static real permittivity (median MAE and MSE improvement ≈39–63%).
• Low-energy (0–8 eV) improvements: Gains are comparably strong and are especially relevant for thin-film optical materials screening.
• Similarity Coefficient (SC): Absolute improvements are modest but statistically consistent (≈1–1.4%), reflecting subtle yet systematic gains in spectral fidelity.
• GNNOpt Dataset: In low-data settings, GotenNetOpt yields 12–22% improvements in MSE and R² across both spectral components relative to GNNOpt.

Architectural and Feature Ablations

• Model Size: The smaller GotenNetOpt-S performs only 6–7% worse than full-scale GotenNetOpt, supporting the contention that architectural, not parametric, expressiveness is the main driver of improvement.
• Graph Construction: Distance-based cutoff graphs provide ≈4% better performance than Voronoi-based graphs across targets.
• Covalent Radius Ablation: Inclusion yields modest improvements (up to 4% in RPA targets), especially pertinent for many-body accurate spectra.

Failure Analysis

Prediction accuracy exhibits a log-linear dependence on per-element training frequency, validating and extending findings from OptiMate3B. Elements with scarce representation (e.g., Kr) result in outlier errors due to poorly conditioned embeddings and physically uninformative features (e.g., meaningless covalent radius).

Implications and Forward Directions

Practical Impact

The demonstrated improvements, especially in the low-energy spectral regime and static permittivity, directly enhance the viability of ML-based materials screening pipelines for optics and photovoltaics. Equivariant message passing ensures that models can learn physically consistent representations without explicit symmetry encoding, which becomes increasingly critical as datasets grow in chemical and structural diversity.

Theoretical Significance

The results highlight the value of geometric inductive biases in atomistic ML, particularly when training data is physically accurate and limited. The superiority of equivariant architectures over rotation-invariant ones, especially in encoding many-body and angular correlations, suggests broader applicability for other tensorial property prediction tasks.

Future Research

Several promising avenues remain:

• Atomic Feature Engineering: Exploring additional physically motivated descriptors (e.g., polarization, magnetic moments) optimized for task-specific subspaces.
• Equivariant Architecture Exploration: Benchmarking other SO(3)-equivariant GNNs (e.g., MACE, Equiformer) for optical and other tensorial property prediction.
• Data Expansion and Transfer Learning: Increasing coverage for underrepresented elements and leveraging transfer learning from larger, heterogeneous datasets.
• Readout Layer Optimization: Investigating alternative graph-level pooling mechanisms to further improve spectral prediction fidelity.

Conclusion

The adaptation of GotenNet for optical spectra prediction demonstrates that equivariant GNNs provide a robust geometric inductive bias, yielding consistent gains over invariant baseline architectures. Performance improvements are most pronounced for physically accurate (RPA) spectra and in spectroscopically relevant energy ranges. For high-throughput materials screening, especially in thin-film optics, this approach advances the accuracy and expressiveness of ML surrogates, laying the groundwork for further exploration of equivariant architectures and feature engineering in property prediction. The dominant limitation remains coverage gaps for rare elements; targeted expansion of training data will be required to fully leverage these models for unexplored chemical spaces.