mlsanityData to 7 Oct 2026

Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics

arXiv 2009.08551 ↗First posted 17 Sep 2020physics.comp-ph cs.LGcited by 36

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Abstract (arXiv)

Including prior knowledge is important for effective machine learning models in physics, and is usually achieved by explicitly adding loss terms or constraints on model architectures. Prior knowledge embedded in the physics computation itself rarely draws attention. We show that solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides an implicit regularization that greatly improves generalization. Two separations suffice for learning the entire one-dimensional H2 dissociation curve within chemical accuracy, including the strongly correlated region. Our models also generalize to unseen types of molecules and overcome self-interaction error.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Sep 2020.

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Citing papers per year: 2021: 11; 2022: 8; 2023: 6; 2024: 7; 2025: 1; 2026: 3.

36 papers.

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  1. 2021Machine learning accelerated computational fluid dynamicscited by 461
  2. 2021Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modelingcited by 59
  3. 2022SchNetPack 2.0: A neural network toolbox for atomistic machine learningcited by 29
  4. 2021Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistrycited by 27
  5. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  6. 2021Learning the exchange-correlation functional from nature with fully differentiable density functional theorycited by 23
  7. 2022Evolving symbolic density functionalscited by 19
  8. 2021Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Futurecited by 18
  9. 2021Differentiable Physics: A Position Piececited by 12
  10. 2023Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learningcited by 11
  11. 2021Physics perception in sloshing scenes with guaranteed thermodynamic consistencycited by 10
  12. 2021Audacity of huge: overcoming challenges of data scarcity and data quality for machine learning in computational materials discoverycited by 10
24 more
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  2. 2022A composable machine-learning approach for steady-state simulations on high-resolution gridscited by 8
  3. 2024Image Super-resolution Inspired Electron Density Predictioncited by 8
  4. 2025Accurate and scalable exchange-correlation with deep learningcited by 8
  5. 2021DQC: a Python program package for Differentiable Quantum Chemistrycited by 7
  6. 2023D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theorycited by 6
  7. 2024Learning Equivariant Non-Local Electron Density Functionalscited by 6
  8. 2024Reducing the Cost of Quantum Chemical Data By Backpropagating Through Density Functional Theorycited by 4
  9. 2021A composable autoencoder-based iterative algorithm for accelerating numerical simulationscited by 3
  10. 2021How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?cited by 3
  11. 2022A Transferable Recommender Approach for Selecting the Best Density Functional Approximations in Chemical Discoverycited by 3
  12. 2023Variational principle to regularize machine-learned density functionals: the non-interacting kinetic-energy functionalcited by 2
  13. 2026Derivative Informed Learning of Exchange-Correlation Functionalscited by 2
  14. 2023Grad DFT: a software library for machine learning enhanced density functional theorycited by 1
  15. 2024Physics-integrated generative modeling using attentive planar normalizing flow based variational autoencodercited by 1
  16. 2024NeuralSCF: Neural network self-consistent fields for density functional theorycited by 1
  17. 2024Data-driven Modeling in Metrology -- A Short Introduction, Current Developments and Future Perspectivescited by 1
  18. 2022Self-consistent Gradient-like Eigen Decomposition in Solving Schr"odinger Equationscited by 0
  19. 2022AD-NEGF: An End-to-End Differentiable Quantum Transport Simulator for Sensitivity Analysis and Inverse Problemscited by 0
  20. 2023Generating QM1B with PySCFIPUcited by 0
  21. 2023Deep Learning with Physics Priors as Generalized Regularizerscited by 0
  22. 2024Machine learning approach for vibronically renormalized electronic band structurescited by 0
  23. 2026A fully differentiable framework for training proxy Exchange Correlation Functionals for periodic systemscited by 0
  24. 2026Benchmarking Optimizers to Solve Inverse Problems with Differentiable Physics Simulatorscited by 0