Fig. 1: Computational framework.
From: Towards the ground state of molecules via diffusion Monte Carlo on neural networks
a A sketch of a brief overview on variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) from the perspective of eigenstates composition. Atomic orbitals represent different eigenstates, and histograms indicate the weight of each eigenstate in the state decomposition. Top: A randomly initialized state with no dominant eigenstate. Middle: The output state of VMC where the ground state dominates, but other eigenstates are still non-negligible due to ansatz limitations. Bottom: The output state of DMC, which surpasses ansatz limitations and reaches the ground state. b Left: a neural network ansatz of wavefunction; right: one dimensional projection of a many-electron wavefunction and its nodal surface. c Left: parallelized diffusion Monte Carlo processes on GPU; right: zoom in to the stochastic dynamics of each walker containing configurations of all electrons in the system, while the nodal structure is fixed. This panel is inspired by and adapted with permission from the website of Quantum Monte Carlo for Chemistry @ Toulouse (http://qmcchem.ups-tlse.fr/index.php/Quantum_Monte_Carlo_for_Chemistry_@_Toulouse)56. d Three key steps in diffusion Monte Carlo. Each walker is assigned with a weight, which evolves every iteration. Diffuse: The stochastic propagation of walkers without crossing the nodal surface. Branch: Split one walker when its weight becomes too large. Merge: Merge two walkers when their weights become too small.
