Deep learning and the Schrödinger equation
This work addresses the challenge of solving the Schrödinger equation for complex potentials in quantum chemistry, though it is incremental as it applies existing deep learning methods to a specific domain.
The authors tackled the problem of predicting ground-state energies of electrons in random 2D electrostatic potentials using a deep convolutional neural network, achieving chemical accuracy with a median absolute error of 1.49 mHa.
We have trained a deep (convolutional) neural network to predict the ground-state energy of an electron in four classes of confining two-dimensional electrostatic potentials. On randomly generated potentials, for which there is no analytic form for either the potential or the ground-state energy, the neural network model was able to predict the ground-state energy to within chemical accuracy, with a median absolute error of 1.49 mHa. We also investigate the performance of the model in predicting other quantities such as the kinetic energy and the first excited-state energy of random potentials.