# Self-Refining Training for Amortized Density Functional Theory

arXiv: https://arxiv.org/abs/2506.01225 · HTML: https://mlsanity.com/paper/2506.01225/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation](https://mlsanity.com/paper/2410.22388/) (2024)
- [Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian](https://mlsanity.com/paper/2306.04922/) (2023)
- [Towards Foundational Models for Molecular Learning on Large-Scale Multi-Task Datasets](https://mlsanity.com/paper/2310.04292/) (2023)
- [Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning](https://mlsanity.com/paper/2309.16578/) (2023)
- [Self-Consistency Training for Density-Functional-Theory Hamiltonian Prediction](https://mlsanity.com/paper/2403.09560/) (2024)
- [DQC: a Python program package for Differentiable Quantum Chemistry](https://mlsanity.com/paper/2110.11678/) (2021)
- [D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory](https://mlsanity.com/paper/2303.00399/) (2023)
- [Reducing the Cost of Quantum Chemical Data By Backpropagating Through Density Functional Theory](https://mlsanity.com/paper/2402.04030/) (2024)
- [MESS: Modern Electronic Structure Simulations](https://mlsanity.com/paper/2406.03121/) (2024)

## Built on by (most cited first, 1 of 1)

- [Scaling Density Functional Theory with Gaussian Splatting](https://mlsanity.com/paper/2609.31483/) (2026)

## Abstract (arXiv)

Density Functional Theory (DFT) allows for predicting all the chemical and physical properties of molecular systems from first principles by finding an approximate solution to the many-body Schr"odinger equation. However, the cost of these predictions becomes infeasible when increasing the scale of the energy evaluations, e.g., when calculating the ground-state energy for simulating molecular dynamics. Recent works have demonstrated that, for substantially large datasets of molecular conformations, Deep Learning-based models can predict the outputs of the classical DFT solvers by amortizing the corresponding optimization problems. In this paper, we propose a novel method that reduces the dependency of amortized DFT solvers on large pre-collected datasets by introducing a self-refining training strategy. Namely, we propose an efficient method that simultaneously trains a deep-learning model to predict the DFT outputs and samples molecular conformations that are used as training data for the model. We derive our method as a minimization of the variational upper bound on the KL-divergence measuring the discrepancy between the generated samples and the target Boltzmann distribution defined by the ground state energy. To demonstrate the utility of the proposed scheme, we perform an extensive empirical study comparing it with the models trained on the pre-collected datasets. Finally, we open-source our implementation of the proposed algorithm, optimized with asynchronous training and sampling stages, which enables simultaneous sampling and training. Code is available at https://github.com/majhas/self-refining-dft.