Accelerating the Optimization of Neural Network Wavefunctions in First Quantization
Gil Goldshlager, University of California, Berkeley
The electronic structure problem refers to the challenge of simulating electrons as systems of interacting quantum particles under the influence of fixed atomic nuclei. Accurate and efficient algorithms for the electronic structure problem can accelerate progress on both basic science and practical applications across the fields of chemistry, materials science, and condensed matter physics. Existing electronic structure methods can reliably simulate weakly correlated molecules in which the electrons do not deviate too strongly from a mean-field assumption. However, no existing method can reliably predict the electronic structure of strongly correlated molecules containing more than a few tens of electrons. Recently, neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce some of the most accurate ever descriptions of the electronic structure of small but strongly correlated molecules. This presents the promise of breaking new ground in strongly correlated quantum chemistry if this approach can be scaled up to larger systems. The challenge is that within this paradigm, simulating even a single molecular configuration requires an expensive stochastic optimization procedure. Within this optimization procedure, the asymptotic bottleneck is the cost of estimating the kinetic energy of the wavefunction, which scales quartically with the number of electrons. In this work we present an approach for reducing this quartic scaling to cubic scaling by modifying the way that the kinetic energy is estimated. We demonstrate the efficacy of this approach on toy systems and identify the key barriers to applying it to practical calculations.
Abstract Author(s): Gil Goldshlager, Zhiyan Ding, Nilin Abrahamsen, Lin Lin