Authors: Kasper Helverskov Petersen, François R J Cornet, Martin Ovesen, Mikkel Jordahn, Kristian S. Thygesen, Mikkel N. Schmidt
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.
We introduce a spectral-injection diagnostic for measuring which angular frequencies a trained equivariant force-field backbone preserves: inject a controlled angular-frequency perturbation into a molecular force field, attach a lightweight Spectral Prediction Network (SPN) to the frozen backbone, and read off which frequencies are recoverable. On aspirin, a quadratic SPN attached to an L = 2 NequIP backbone recovers the boundary signal at l = 4 but collapses at l = 5: a 11.7x cliff at the predicted drL boundary, with p dropping from 0.913 to 0.078. The same boundary-vs-above contrast persists across n = 4 independently trained backbones (raw-gain delta contrast, hierarchical cluster bootstrap) and is corroborated by a denominator-free injected-residual metric (R2_inj(4) = 0.374 versus R2_inj(5) = 0.006). A finite-degree span theorem calibrates the diagnostic: for a single marked direction, degree-d polynomials of degree-L spherical-harmonic features span exactly H less than or equal to dL with multiplicity-one saturation at the boundary (scoped to single-direction degree-bounded probes, not a function-class upper bound on multi-atom MPNNs). A synthetic C5 calibration plus capacity, activation, and cross-architecture controls rule out parameter count alone as the explanation.
Predicting a material's properties from its structure is a central, fast-advancing problem in computational materials science. A decade of work has produced standard public benchmarks and many published machine-learning models for the task (Dunn et al., 2020). The task's fixed metric and these baselines make it a natural setting for autonomous agent research (Karpathy, 2026). On the MatBench band-gap benchmark (>100k crystals), a general-purpose coding agent autonomously built the most accurate model trained without external pretraining, ahead of all seventeen expert-designed models reported for the task. A closer analysis shows it reached this by implementing known methods: either already standard in crystal neural-network models, or borrowed from other areas of machine learning. The contributing implementations include element-pair features on each message-passing edge and a crystal space-group embedding. The work not only demonstrates that LLM-agent autonomous research can optimize an expert-designed machine learning model for material property prediction, but also investigates the limitations of such autonomous research.
Pre-trained materials foundation models, or machine learning interatomic potentials, leverage general physicochemical knowledge to effectively approximate potential energy surfaces. However, they often require domain-specific calibration due to physicochemical diversity as well as mismatches between practical computational settings and those used in constructing the pre-training data. To address this, we propose a sparsity-promoting fine-tuning method that selectively updates model parameters by exploiting the structural properties of E(3)-equivariant materials foundation models. On energy and force prediction tasks across molecular and crystalline benchmarks, our method matches or surpasses full fine-tuning and equivariant low-rank adaptation while updating only ∼3~% of parameters, and in some cases as little as ∼0.5~%. Beyond energy and force calibration, we further demonstrate task generalizability by applying our method to magnetic moment prediction and magnetism-aware total energy modeling. Finally, analysis of sparsity patterns reveals physically interpretable signatures, such as enhanced d-orbital contributions in transition metal systems. Overall, our results establish sparsity-promoting fine-tuning as a flexible and interpretable method for domain specialization of equivariant materials foundation models.