mlsanityData to 7 Oct 2026

By-passing the Kohn-Sham equations with machine learning

arXiv 1609.02815 ↗First posted 9 Sep 2016physics.comp-ph cs.LG physics.chem-phcited by 65

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Abstract (arXiv)

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to astrophysics. Machine learning holds the promise of learning the kinetic energy functional via examples, by-passing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing either larger systems or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. Both improved accuracy and lower computational cost with this method are demonstrated by reproducing DFT energies for a range of molecular geometries generated during molecular dynamics simulations. Moreover, the methodology could be applied directly to quantum chemical calculations, allowing construction of density functionals of quantum-chemical accuracy.

Key facts. Cited by 65 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Sep 2016.

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Citing papers per year: 2021: 10; 2022: 15; 2023: 13; 2024: 8; 2025: 7; 2026: 12.

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  1. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  2. 2022SchNetPack 2.0: A neural network toolbox for atomistic machine learningcited by 29
  3. 2021Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solidscited by 24
  4. 2022DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulationscited by 24
  5. 2021Learning the exchange-correlation functional from nature with fully differentiable density functional theorycited by 23
  6. 2022Evolving symbolic density functionalscited by 19
  7. 2021Machine learning nonequilibrium electron forces for adiabatic spin dynamicscited by 17
  8. 2022Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systemscited by 16
  9. 2023Physics-inspired Equivariant Descriptors of Non-bonded Interactionscited by 13
  10. 2023Higher-Order Equivariant Neural Networks for Charge Density Prediction in Materialscited by 12
  11. 2023Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learningcited by 11
  12. 2021Audacity of huge: overcoming challenges of data scarcity and data quality for machine learning in computational materials discoverycited by 10
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  1. 2023Equivariant Neural Operator Learning with Graphon Convolutioncited by 10
  2. 2025ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitalscited by 9
  3. 2021Bayesian neural networks for weak solution of PDEs with uncertainty quantificationcited by 8
  4. 2021Geometric Transformer for End-to-End Molecule Properties Predictioncited by 8
  5. 2024Image Super-resolution Inspired Electron Density Predictioncited by 8
  6. 2024A Recipe for Charge Density Predictioncited by 8
  7. 2024Scalable Training of Trustworthy and Energy-Efficient Predictive Graph Foundation Models for Atomistic Materials Modeling: A Case Study with HydraGNNcited by 8
  8. 2023Wigner kernels: body-ordered equivariant machine learning without a basiscited by 7
  9. 20233DReact: Geometric deep learning for chemical reactionscited by 7
  10. 2022Prediction of the electron density of states for crystalline compounds with Atomistic Line Graph Neural Networks (ALIGNN)cited by 6
  11. 2022Embed and Emulate: Learning to estimate parameters of dynamical systems with uncertainty quantificationcited by 5
  12. 2023Towards Combinatorial Generalization for Catalysts: A Kohn-Sham Charge-Density Approachcited by 5
  13. 2022Electronic-structure properties from atom-centered predictions of the electron densitycited by 4
  14. 2021Deep learning for surrogate modelling of 2D mantle convectioncited by 3
  15. 2021How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?cited by 3
  16. 2022Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Spacecited by 3
  17. 2022Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discoverycited by 3
  18. 2023Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimensioncited by 3
  19. 2023Alpha Zero for Physics: Application of Symbolic Regression with Alpha Zero to find the analytical methods in physicscited by 3
  20. 2022Accelerating hypersonic reentry simulations using deep learning-based hybridization (with guarantees)cited by 2
  21. 2022The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfacescited by 2
  22. 2023Machine learning for accuracy in density functional approximationscited by 2
  23. 2023Electronic excited states from physically-constrained machine learningcited by 2
  24. 2024Accelerating Electron Dynamics Simulations through Machine Learned Time Propagatorscited by 2
  25. 2025Towards A Transferable Acceleration Method for Density Functional Theorycited by 2
  26. 2022Molecular Dipole Moment Learning via Rotationally Equivariant Gaussian Process Regression with Derivatives in Molecular-orbital-based Machine Learningcited by 1
  27. 2022Molecular-orbital-based Machine Learning for Open-shell and Multi-reference Systems with Kernel Addition Gaussian Process Regressioncited by 1
  28. 2023Grad DFT: a software library for machine learning enhanced density functional theorycited by 1
  29. 2024NeuralSCF: Neural network self-consistent fields for density functional theorycited by 1
  30. 2025Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theorycited by 1
  31. 2025Machine Learning Time Propagators for Time-Dependent Density Functional Theory Simulationscited by 1
  32. 2025Synergizing chemical and AI communities for advancing laboratories of the futurecited by 1
  33. 2026Machine learning nonequilibrium phase transitions in charge-density wave insulatorscited by 1
  34. 2026Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blinkcited by 1
  35. 2026M=oLe-Lambda: Learning the Coupled-Cluster Response State for Energies, Gradients, and Propertiescited by 1
  36. 2026Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theorycited by 1
  37. 2021Reducing the Long Tail Losses in Scientific Emulations with Active Learningcited by 0
  38. 2022Machine Learning Diffusion Monte Carlo Energiescited by 0

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