Kohn-Sham Equations as Regularizer: Building Prior Knowledge into Machine-Learned Physics

SciPy 1.0: fundamental algorithms for scientific computing in Python

(2020) Pauli Virtanen et al.   NATURE METHODS

Completing density functional theory by machine learning hidden messages from molecules

(2020) Ryo Nagai et al.   npj Computational Materials

Deep Learning the Hohenberg-Kohn Maps of Density Functional Theory

(2020) Javier Robledo Moreno et al.   PHYSICAL REVIEW LETTERS

Deep-neural-network solution of the electronic Schrödinger equation

(2020) Jan Hermann et al.   Nature Chemistry

Screening billions of candidates for solid lithium-ion conductors: A transfer learning approach for small data

(2019) Ekin D. Cubuk et al.   JOURNAL OF CHEMICAL PHYSICS

Learning data-driven discretizations for partial differential equations

(2019) Yohai Bar-Sinai et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning

(2019) Frank Noé et al.   SCIENCE

Differentiable Programming Tensor Networks

(2019) Hai-Jun Liao et al.   Physical Review X

Machine Learning the Physical Nonlocal Exchange–Correlation Functional of Density-Functional Theory

(2019) Jonathan Schmidt et al.   Journal of Physical Chemistry Letters

Toward the Exact Exchange–Correlation Potential: A Three-Dimensional Convolutional Neural Network Construct

(2019) Yi Zhou et al.   Journal of Physical Chemistry Letters

Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions

(2019) K. T. Schütt et al.   Nature Communications

Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability

(2018) Ryo Nagai et al.   JOURNAL OF CHEMICAL PHYSICS

Can exact conditions improve machine-learned density functionals?

(2018) Jacob Hollingsworth et al.   JOURNAL OF CHEMICAL PHYSICS

Sigmoid-weighted linear units for neural network function approximation in reinforcement learning

(2018) Stefan Elfwing et al.   NEURAL NETWORKS

Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree–Fock

(2018) Teresa Tamayo-Mendoza et al.   ACS Central Science

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical methods for the inverse problem of density functional theory

(2017) Daniel S. Jensen et al.   INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals

(2017) Narbe Mardirossian et al.   MOLECULAR PHYSICS

Bypassing the Kohn-Sham equations with machine learning

(2017) Felix Brockherde et al.   Nature Communications

Optimal Rates for Zero-Order Convex Optimization: The Power of Two Function Evaluations

(2015) John C. Duchi et al.   IEEE TRANSACTIONS ON INFORMATION THEORY

Understanding machine-learned density functionals

(2015) Li Li et al.   INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

Deep learning

(2015) Yann LeCun et al.   NATURE

One-dimensional mimicking of electronic structure: The case for exponentials

(2015) Thomas E. Baker et al.   PHYSICAL REVIEW B

Density functional theory: Its origins, rise to prominence, and future

(2015) R. O. Jones   REVIEWS OF MODERN PHYSICS

Gedanken densities and exact constraints in density functional theory

(2014) John P. Perdew et al.   JOURNAL OF CHEMICAL PHYSICS

Guaranteed Convergence of the Kohn-Sham Equations

(2013) Lucas O. Wagner et al.   PHYSICAL REVIEW LETTERS

Derivative-free optimization: a review of algorithms and comparison of software implementations

(2012) Luis Miguel Rios et al.   JOURNAL OF GLOBAL OPTIMIZATION

One-Dimensional Continuum Electronic Structure with the Density-Matrix Renormalization Group and Its Implications for Density-Functional Theory

(2012) E. M. Stoudenmire et al.   PHYSICAL REVIEW LETTERS

Finding Density Functionals with Machine Learning

(2012) John C. Snyder et al.   PHYSICAL REVIEW LETTERS

Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning

(2012) Matthias Rupp et al.   PHYSICAL REVIEW LETTERS

Insights into Current Limitations of Density Functional Theory

(2008) A. J. Cohen et al.   SCIENCE