Advancing Machine Learning Applications in Quantum Few-Body Systems

Abstract

This paper presents a general neural network framework for solving quantum few-body systems, extending prior methods to handle diverse particle masses, interaction types, and system configurations. Our architecture, which combines an adaptive step size with the Metropolis-Adjusted Langevin Algorithm for Monte Carlo sampling, accurately approximates the ground-state wave functions of systems featuring harmonic confinement, Gaussian two-body interactions, and including three-body forces. In ten-particle systems, it achieves lower relative energy errors (with respect to the reference values) than previous machine-learning methods. Leveraging GPU-accelerated computation, the method scales favorably with system size while maintaining robust convergence, reduced hyperparameter sensitivity, and stable training. Beyond accurate energy estimation, the model captures spatial distributions and correlation structures, offering physical insights about inter-particle structure. By unifying applicability across identical and nonidentical particles, the proposed approach establishes a versatile computational tool for exploring complex few-body quantum systems, with significant implications for advancing computational models in few-body quantum systems.

Figures (26)

• Figure 1: Architecture of the multilayer perceptron used for quantum wavefunction approximation. The network takes interparticle distances as input and outputs the wavefunction amplitude. The exponential output activation ensures positive wavefunction values suitable for bosonic ground states.
• Figure 2: Schematic diagram of the Neural Network architecture. The network accepts inter-particle distances as input, processes them through hidden layers, and outputs a single amplitude value using an exponential function.
• Figure 3: Energy training convergence for 3-particle harmonic potential systems with two-body interactions. The blue line represents the mean energy ($E_{\mathrm{mean}}$) across five independent trials, while the shaded blue region indicates the range between the minimum and maximum values among these trials. The red dashed line denotes the reference energy.
• Figure 4: Energy training convergence for 8-particle harmonic potential systems with two-body interactions.
• Figure 5: Performance metrics for harmonic potential systems. (a) Coefficient of variation of energy across particle numbers for 5 runs, showing improved consistency as system size increases for adaptive sampling methods. (b) Relative error in energy estimation across different particle numbers, comparing GELU-MALA (blue) and GELU-ARW (red) from five independent test runs.