Project Summary

Machine learning interatomic potentials (MLIP) can speed-up DFT by 1000x and unlock accurate ab-intio simulations of large systems such as proteins.

Current MLIPs are trained using supervision from datasets derived from DFT. Creating such datasets is expensive. Further, datasets labelled with different functionals or even different version numbers of the DFT code are incompatible, limiting the ability of the community to scale MLIPs.

Here, we devise a fundamentally new way of training MLIPs without needing to pre-calculate data for supervision.

The key insight is that a DFT calculation already contains a minimisation step of the Hamiltonian with respect to the energy density. This minimisation step can be skipped by using the Hamiltonian directly in the loss function, skipping the generation of the ground state.  

This project scales this approach to create a training strategy for universal machine learning interatomic potentials that can be used (1) across the periodic table and (2) for systems with over 100,000 atoms.  

On the way towards 100,000 atoms, we have the opportunity to devise training strategies, scaling laws and uncertainty quantification algorithms to understand when to backpropagate. We will investigate efficient architectures and drive down the cost of inference. On the physics side, we will understand the learned world models and improve its ability to generalise out of distribution. We will look at including electron correlation, looking beyond the ground state and extending the loss beyond the Hamiltionian to dynamic properties, such as backpropagating through a free energy functional.

This is an ambitious project and the capabilities that it will create will be essential to building a continually learning simulation software, which uses a foundation model to drive sampling, dynamics and electronic property calculated. With each run, the underlying foundation model can be improved. ‍

‍Potential supervisors

• Dr Flaviu Cipcigan (Research Scientist, EIT)
• Additional Supervisor(s) from the University of Oxford

Skills Recommended

• Strong background in DFT
• Strong background in neural network training
• Advanced quantum mechanics and statistical physics training
• Strong coding skills in Python and expertise with PyTorch / JAX

Skills to be Developed

• Designing novel neural network architectures
• Designing novel neural network training methods
• Developing next-generation ML interatomic potentials
• Physics inspired machine learning

University DPhil Courses 

• DPhil in Materials  ‍
• DPhil in Chemistry  ‍
• DPhil in Computer Science  

Relevant Background Reading

• Mathiasen, A. et al. Reducing the Cost of Quantum Chemical Data By Backpropagating Through Density Functional Theory. arXiv (2024) doi:10.48550/arxiv.2402.04030.
• Li, Y. et al. Neural-network Density Functional Theory Based on Variational Energy Minimization. arXiv (2024) doi:10.48550/arxiv.2403.11287.
• Zhang, H. et al. Self-Consistency Training for Density-Functional-Theory Hamiltonian Prediction. arXiv (2024) doi:10.48550/arxiv.2403.09560.
• Wang, Z. et al. Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Models. arXiv (2024) doi:10.48550/arxiv.2406.03794.
• Hassan, M., Gabellini, C., Helal, H., Beaini, D. & Neklyudov, K. Self-Refining Training for Amortized Density Functional Theory. arXiv (2025) doi:10.48550/arxiv.2506.01225.
• Yuan, Z. et al. Deep learning density functional theory Hamiltonian in real space. arXiv (2024) doi:10.48550/arxiv.2407.14379.
• Gong, X. et al. General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian. Nat. Commun. 14, 2848 (2023).
• Song, F. & Feng, J. NeuralSCF: Neural network self-consistent fields for density functional theory. arXiv (2024) doi:10.48550/arxiv.2406.15873.
• Schütt, K. T., Gastegger, M., Tkatchenko, A., Müller, K.-R. & Maurer, R. J. Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions. Nat. Commun. 10, 5024 (2019).
• Luo, E. et al. Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity. arXiv (2025) doi:10.48550/arxiv.2502.01171.  
• Pfau, D., Spencer, J. S., Matthews, A. G. D. G. & Foulkes, W. M. C. Ab initio solution of the many-electron Schrödinger equation with deep neural networks. Phys. Rev. Res. 2, 033429 (2020).
• Kim, S., Kim, N., Kim, D. & Ahn, S. High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Prediction. arXiv (2025) doi:10.48550/arxiv.2505.18817.