# Accelerating superconductor discovery through tempered deep learning of the electron-phonon spectral function

arXiv: https://arxiv.org/abs/2401.16611 · HTML: https://mlsanity.com/paper/2401.16611/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 81 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 11 of 11)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Rethinking Bias-Variance Trade-off for Generalization of Neural Networks](https://mlsanity.com/paper/2002.11328/) (2020)
- [Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties](https://mlsanity.com/paper/2008.08461/) (2020)
- [Benign, Tempered, or Catastrophic: A Taxonomy of Overfitting](https://mlsanity.com/paper/2207.06569/) (2022)
- [Machine learning modeling of superconducting critical temperature](https://mlsanity.com/paper/1709.02727/) (2017)
- [Automatic extraction of materials and properties from superconductors scientific literature](https://mlsanity.com/paper/2210.15600/) (2022)

## Built on by (most cited first, 2 of 2)

- [AI-driven inverse design of materials: Past, present and future](https://mlsanity.com/paper/2411.09429/) (2024)
- [Guided Diffusion for the Discovery of New Superconductors](https://mlsanity.com/paper/2509.25186/) (2025)

## Abstract (arXiv)

Integrating deep learning with the search for new electron-phonon superconductors represents a burgeoning field of research, where the primary challenge lies in the computational intensity of calculating the electron-phonon spectral function, α2F(ω), the essential ingredient of Midgal-Eliashberg theory of superconductivity. To overcome this challenge, we adopt a two-step approach. First, we compute α2F(ω) for 818 dynamically stable materials. We then train a deep-learning model to predict α2F(ω), using an unconventional training strategy to temper the model's overfitting, enhancing predictions. Specifically, we train a Bootstrapped Ensemble of Tempered Equivariant graph neural NETworks (BETE-NET), obtaining an MAE of 0.21, 45 K, and 43 K for the Eliashberg moments derived from α2F(ω): λ, ωlog, and ω2, respectively, yielding an MAE of 2.5 K for the critical temperature, Tc. Further, we incorporate domain knowledge of the site-projected phonon density of states to impose inductive bias into the model's node attributes and enhance predictions. This methodological innovation decreases the MAE to 0.18, 29 K, and 28 K, respectively, yielding an MAE of 2.1 K for Tc. We illustrate the practical application of our model in high-throughput screening for high-Tc materials. The model demonstrates an average precision nearly five times higher than random screening, highlighting the potential of ML in accelerating superconductor discovery. BETE-NET accelerates the search for high-Tc superconductors while setting a precedent for applying ML in materials discovery, particularly when data is limited.