Finding Density Functionals with Machine Learning

By John C. Snyder, Matthias Rupp , Katja Hansen, K. Müller, Kieron Burke. 2011

507 citations recorded by the source corpus.

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of noninteracting fermions in 1D, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is within the interpolation region. Via principal component analysis, a projected functional derivative finds highly accurate self-consistent densities. The challenges for application of our method to real electronic structure problems are discussed.

Subfields: Artificial Intelligence, Materials Chemistry, Computational Chemistry & Drug Discovery, AI for Physical Sciences

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. K. Müller
2. Grgoire Montavon
3. Wojciech Samek
4. Kristof T. Schütt
5. Sebastian Lapuschkin
6. Pieter-Jan Kindermans
7. Alexandre Tkatchenko
8. Christopher J. Anders

In Materials Chemistry

1. K. Müller
2. Rampi Ramprasad
3. Grgoire Montavon
4. Rohit Batra
5. Alexander V. Shapeev
6. Evgeny V. Podryabinkin
7. Wojciech Samek
8. Alexandre Tkatchenko

In Computational Chemistry & Drug Discovery

1. K. Müller
2. Grgoire Montavon
3. Wojciech Samek
4. Alexandre Tkatchenko
5. Rampi Ramprasad
6. Kristof T. Schütt
7. Rohit Batra
8. A. Pais

In AI for Physical Sciences

1. K. Müller
2. Grgoire Montavon
3. Wojciech Samek
4. Kristof T. Schütt
5. Alexander V. Shapeev
6. Alexandre Tkatchenko
7. Rampi Ramprasad
8. Evgeny V. Podryabinkin

Citations in the corpus

• Methods for interpreting and understanding deep neural networks (2017, methodology): “More generally, techniques that rely on the function’s gradient, such as sensitivity analysis or simple Taylor decomposition, are more exposed to the derivative noise [45] that characterizes complex machine learning models.”
• SchNet: A continuous-filter convolutional neural network for modeling quantum interactions (2017, background): “Commonly, this can be solved by a re-sampling approach defining a representation on a grid [7, 27, 28].”
• Accurate interatomic force fields via machine learning with covariant kernels (2016, methodology): “Machine learning techniques have been successfully used to predict properties as diverse as atomization energies [11], density functionals [12], Green’s functions [13], electronic transport coefficients [14], potential energy surfaces [15–17], and free-energy landscapes [18].”
• Emerging materials intelligence ecosystems propelled by machine learning (2020, background): “Other attempts to learn the kinetic energy functionals and provide an alternative orbital-free DFT solution have also been made 164 .”