Machine learning the deuteron: new architectures and uncertainty quantification

Abstract

We solve the ground state of the deuteron using a variational neural network ansatz for the wave function in momentum space. This ansatz provides a flexible representation of both the S and the D states, with relative errors in the energy which are within fractions of a percent of a full diagonalisation benchmark. We extend the previous work on this area in two directions. First, we study new architectures by adding more layers to the network and by exploring different connections between the states. Second, we provide a better estimate of the numerical uncertainty by taking into account the final oscillations at the end of the minimisation process. Overall, we find that the best performing architecture is the simple one-layer, state-independent network. Two-layer networks show indications of overfitting, in regions that are not probed by the fixed momentum basis where calculations are performed. In all cases, the error associated to the model oscillations around the real minimum is larger than the stochastic initialisation uncertainties. The conclusions that we draw can be generalised to other quantum mechanics settings.

Hidden-nucleons neural-network quantum states for the nuclear many-body problem

“…[26], where the groundstate of the deuteron is reproduced with remarkable accuracy by a single-layer ANN -see Ref. [27] for a detailed uncertainty-quantification analysis. Subsequently, an anti-symmetric coordinate-space ansatz defined through the product between a permutation-invariant ANNs Jastrow and a Slater determinant of single-particle orbitals has been utilized in a variational Monte Carlo (VMC) method to solve leading-order pionless-EFT Hamiltonians of A ≤ 6 nuclei [28,29].…”

Solving the nuclear pairing model with neural network quantum states

“…Within low-energy nuclear Physics, from their initial applications to solving the deuteron in momentum space [18,19], NQS have been subsequently combined with Variational Monte Carlo (VMC) techniques to approximately solve A ≤ 4 [20] and A ≤ 6 nuclei [21]. Most recently, the hidden-nucleon architecture has been proposed to overcome the limitations of the Slater-Jastrow ansatz and successfully applied to nuclei up to 16 O [22].…”