Ab initio solution of the many-electron Schrödinger equation with deep neural networks

Abstract

Given access to accurate solutions of the many-electron Schrödinger equation, nearly all chemistry could be derived from first principles. Exact wave functions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially scaling algorithms. The key challenge for many of these algorithms is the choice of wave function approximation, or Ansatz, which must trade off between efficiency and accuracy. Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wave-function Ansatz for spin systems, but problems in electronic structure require wave functions that obey Fermi-Dirac statistics. Here we introduce a novel deep learning architecture, the Fermionic neural network, as a powerful wave-function Ansatz for many-electron systems. The Fermionic neural network is able to achieve accuracy beyond other variational quantum Monte Carlo Ansatz on a variety of atoms and small molecules. Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry. This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab initio quantum chemistry methods, opening the possibility of accurate direct optimization of wave functions for previously intractable many-electron systems.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

“…Construction of efficient and reliable antisymmetric ML models for the many-body wavefunction is an important area of current research. 104 , 105 …”

“…Efforts are beginning to become implemented that use ML to accelerate these types of calculations. 104 , 105 , 124 − 128 …”

Interactions between large molecules pose a puzzle for reference quantum mechanical methods

“…In principle, a more flexible wavefunction ansatz allows a more accurate many-body wavefunction to be reached in DMC, thus recovering electron correlation more effectively. To this end, recently introduced machine learning approaches 80,81 are promising but more expensive due to the considerable increase in parameters. However, once feasible, a systematic assessment of the amount of electron correlation recovered by these different ansatze in non-covalently bound systems will bring valuable insight to the current puzzle.…”

Perspective on integrating machine learning into computational chemistry and materials science

“…First attempts to solve non-homogeneous ordinary and partial differential equations using ML algorithms 6,[110][111][112] already date back to more than 20 years ago for model systems and have recently been applied to solve the quantum many-body problem for small organic molecular systems. [113][114][115][116][117][118][119][120] These efforts have recently been summarized in a comprehensive review 16 and perspective. 25 While they are conceptually exciting and potentially transformative in solving the many body problem, their integration into existing, widely accessible electronic structure software may not be fully practicable yet as existing models are limited to small system sizes and not yet transferable.…”