shared HamEPC a while back with a note that it might help close the gap between crystal generation and Tc prediction. Since then, the field has moved fast enough that it's worth an update on where things stand.
The core bottleneck in computational superconductor discovery has always been the electron-phonon coupling calculation. DFPT is accurate but brutally expensive — you can generate thousands of candidate structures but only afford to run EPC calculations on a handful. That asymmetry is what HamEPC targets: by learning the Hamiltonian in an atomic-orbital basis (via HamGNN), it can predict phonon-electron matrix elements in a fraction of the DFT time.
What's changed recently is that two other approaches have arrived that attack the same problem from different angles, and together they suggest the field is converging on something usable.
BETE-NET (published in npj Computational Materials, Jan 2025) takes a different tack: instead of learning the Hamiltonian, it learns the Eliashberg spectral function
Uni-HamGNN (published in Nature Machine Intelligence, 2026) extends the HamGNN approach to include spin-orbit coupling, which matters enormously for heavy-element systems and topological materials. The original HamGNN was limited to systems without SOC, which ruled out a large swath of interesting candidates. The ability to handle SOC in a graph-neural-network Hamiltonian framework opens the door to screening across the full periodic table, including the actinides and heavy transition metals where some of the more exotic superconductors live.
What's interesting about this convergence is that the three approaches are complementary rather than competing. Uni-HamGNN gives you accurate electronic structure (including SOC) without running full DFT. BETE-NET lets you predict and thus without running DFPT at all. HamEPC sits between them, bridging the Hamiltonian representation to phonon coupling. You could imagine a pipeline where Uni-HamGNN generates the electronic structure, HamEPC computes the coupling matrix, and BETE-NET validates the resulting prediction — each step acting as a prior for the next.
The remaining hard problem is the dataset. All of these models are trained on relatively small corpora of DFT-validated superconductors, and the known superconductor space has a severe class imbalance: most compounds simply don't superconduct, and the ones that do span many different mechanisms. BETE-NET's 99.4% true-negative rate is impressive, but it means the model has learned primarily to say "no." Finding the rare yes — especially outside the training distribution, which is where the interesting discoveries live — is where even these new tools remain limited.
The supercell approach that has been exploring for crystal generation is relevant here too. If you can generate larger, more realistic structures, you get more atoms per inference pass, which both reduces the per-atom cost of these Hamiltonian calculations and opens the door to defect and doping effects that could shift in unexpected ways. The generation and evaluation halves of this pipeline are maturing at roughly the same pace, which is encouraging.
The full HamEPC paper is on Zenodo: zenodo.org/records/12685941. BETE-NET code is available alongside the npj paper, and Uni-HamGNN code is linked in the Nature Machine Intelligence publication.
How a new generation of ML models is finally making the electron-phonon bottleneck tractable — and what it means for superconductor search.