Neural Networks Enhance Nuclear Structure Calculations with Variational Monte Carlo.

Neural networks effectively generate trial wave functions for light nuclei, significantly improving the accuracy of variational Monte Carlo calculations. Applied to tritium (³H) with a softened chiral interaction, the network-based approach attains 91% greater accuracy than standard variational Monte Carlo, reaching a ground state energy within 0.45% of results obtained via the more computationally intensive Green’s Function Monte Carlo (GFMC). This demonstrates the potential of machine learning to model complex quantum many-body systems and construct efficient trial wave functions for nuclear physics calculations.

Understanding the forces that bind protons and neutrons within atomic nuclei remains a central challenge in nuclear physics. Accurate modelling necessitates detailed descriptions of the complex correlations arising from the strong nuclear force, a task complicated by the many-body nature of the problem. Researchers are now applying machine learning techniques to refine these calculations, offering a potentially efficient route to constructing accurate wave functions – mathematical descriptions of the quantum state of the nucleus. In a new study published in Physical Review Letters, Pengsheng Wen, Alexandros Gezerlis, and Jeremy W. Holt, from the Cyclotron Institute at Texas A&M University and the University of Guelph, detail a neural network approach to calculating correlation functions for light nuclei. Their work, entitled “Neural-Network Correlation Functions for Light Nuclei with Chiral Two- and Three-Body Interactions”, demonstrates a significant improvement in the accuracy of variational Monte Carlo calculations, bringing results closer to those obtained by the more computationally intensive Green’s Function Monte Carlo method.

Recent research demonstrates a significant advancement in calculating the properties of light nuclei, specifically utilizing neural networks to construct more accurate trial wave functions for variational Monte Carlo (VMC) calculations. These calculations aim to determine the ground state energy and other properties of atomic nuclei, presenting a long-standing challenge in nuclear physics. Researchers currently employ VMC, a stochastic method, to approximate solutions to the complex many-body Schrödinger equation that governs nuclear behavior, and the accuracy of VMC relies heavily on the quality of the trial wave function – an initial guess for the system’s quantum state.

This study introduces a novel approach where neural networks learn to generate these trial wave functions, effectively capturing complex interparticle correlations crucial for accurate results. The team successfully applied this method to tritium (³H), achieving a 91% improvement in ground state energy estimation compared to standard VMC techniques, and this improvement signifies a substantial leap forward in computational nuclear physics. By automating the construction of sophisticated trial wave functions, researchers circumvent the need for extensive manual tuning and parameter optimization, paving the way for more efficient and accurate calculations.

The neural network approach proves particularly effective at modelling the many-body effects arising from three-nucleon interactions – forces acting between all three protons and neutrons simultaneously, and traditional methods often struggle to accurately represent these complex correlations. By learning from data, the neural network constructs wave functions that closely approximate those obtained using the computationally intensive Green’s Function Monte Carlo (GFMC) method, considered a benchmark for accuracy, and this close approximation validates the effectiveness of the neural network approach. The implications of this work are far-reaching, as it opens up new possibilities for studying larger and more complex nuclei that are currently beyond the reach of traditional methods.

Researchers developed a methodology that effectively incorporates complex interparticle correlations and many-body effects, crucial for accurate modelling of nuclear systems, and this methodology represents a significant departure from traditional approaches to nuclear structure calculations. By employing neural networks, the approach efficiently explores the vast parameter space required to define expressive trial wave functions, surpassing the limitations of traditional variational methods, and this efficiency is particularly important for studying heavier nuclei, where the computational cost of traditional methods becomes prohibitive. The successful comparison with GFMC, a benchmark method for nuclear structure, underscores the reliability of the neural network-based approach, establishing a promising pathway for incorporating machine learning into the broader toolkit of computational nuclear physics.

This work highlights the growing synergy between machine learning and nuclear physics, demonstrating the potential of neural networks to address longstanding challenges in the field. The ability to generate accurate trial wave functions with reduced computational effort opens avenues for investigating heavier nuclei and more complex nuclear phenomena, and this advancement facilitates more precise calculations of nuclear properties, contributing to a deeper understanding of the strong nuclear force. Furthermore, the use of neural networks opens up new avenues for exploring the many-body problem in physics, potentially leading to breakthroughs in other areas of condensed matter physics and quantum chemistry.