# Using differentiable programming to obtain an energy and density-optimized exchange-correlation functional

@inproceedings{Dick2021UsingDP, title={Using differentiable programming to obtain an energy and density-optimized exchange-correlation functional}, author={Sebastian Dick and Marivi Fern{\'a}ndez-Serra}, year={2021} }

Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain an accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. We evaluate our model against different families of XC approximations and show that, for non-empirical functionals, there is a…

## 7 Citations

### Generalizability of density functionals learned from differentiable programming on weakly correlated spin-polarized systems

- Computer ScienceArXiv
- 2021

A spin-polarized version of KSR with local, semilocal, and nonlocal approximations for the exchange-correlation functional is proposed, which outperforms any existing machine learning functionals by predicting the ground-state energies of the test systems with a mean absolute error of 2.7 milli-Hartrees.

### Kohn-Sham regularizer for spin density functional theory and weakly correlated systems

- Computer Science
- 2022

The authors' nonlocal functional outperforms any existing machine learning functionals by predicting the ground-state energies of the test systems with a mean absolute error of 2.7 milli-Hartrees.

### D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory

- Computer ScienceArXiv
- 2023

A deep learning approach to KS-DFT is proposed to directly minimize the total energy by reparameterizing the orthogonal constraint as a feed-forward computation, and it is proved that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity from O(N^4) to O(3).

### How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?

- MathematicsThe journal of physical chemistry letters
- 2022

Kohn-Sham regularizer (KSR) is a differentiable machine learning approach to finding the exchange-correlation functional in Kohn-Sham density functional theory that works for strongly correlated…

### Automatic differentiable numerical renormalization group

- PhysicsPhysical Review Research
- 2022

Machine learning techniques have recently gained prominence in physics, yielding a host of new results and insights. One key concept is that of backpropagation, which computes the exact gradient of…

### Evolving symbolic density functionals

- Computer ScienceScience advances
- 2022

A new framework, Symbolic Functional Evolutionary Search (SyFES), is proposed that automatically constructs accurate functionals in the symbolic form, which is more explainable to humans, cheaper to evaluate, and easier to integrate to existing codes than other ML functionals.

### Machine-learning-based exchange correlation functional with physical asymptotic constraints

- Computer SciencePhysical Review Research
- 2022

By applying a novel ML model architecture, this study demonstrates a neural network-based exchange-correlation functional satisfying physical asymptotic constraints and improves the accuracy and generalization performance of the ML-based functional by combining the advantages of ML and analytical modeling.

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