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.

17 pages, 6 figures, 1 table

References in corpus (22)

• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• A high-bias, low-variance introduction to Machine Learning for physicists
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Machine Learning in Nuclear Physics
• Fermionic neural-network states for ab-initio electronic structure
• Nuclear Mass Predictions for the Crustal Composition of Neutron Stars: A Bayesian Neural Network Approach
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Predictions of nuclear $\beta$-decay half-lives with machine learning and their impacts on $r$ process
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Bayesian Evaluation of Incomplete Fission Yields
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Variational Monte Carlo calculations of $\mathbf{A}\le 4$ nuclei with an artificial neural-network correlator ansatz
• Taming nuclear complexity with a committee of multilayer neural networks
• Novel Bayesian neural network based approach for nuclear charge radii
• Machine learning the deuteron
• Method to solve quantum few-body problems with artificial neural networks
• Machine learning-based inversion of nuclear responses
• Nuclei with up to $\mathbf{A}=6$ nucleons with artificial neural network wave functions

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