Normalizing Flows for Microscopic Many-Body Calculations: An Application to the Nuclear Equation of State.

Area of Science:

• Computational Physics
• Machine Learning
• Nuclear Physics

Background:

• Normalizing flows are machine learning models that map simple distributions to complex ones via bijective transformations.
• Quantum many-body calculations often involve high-dimensional integrals with smoothly varying integrands and integration regions.

Purpose of the Study:

• To demonstrate the suitability of normalizing flows as a Monte Carlo integration framework for quantum many-body calculations.
• To leverage normalizing flows for precise evaluations of the nuclear equation of state and related thermodynamic quantities.

Main Methods:

• Utilizing normalizing flows to model complex probability distributions arising in quantum many-body systems.
• Applying the trained normalizing flow models to calculate the nuclear free energy and its derivatives.
• Investigating the transferability of trained models to related integration problems with varied parameters.

Main Results:

• Normalizing flows provide a precise and efficient framework for Monte Carlo integration in quantum many-body problems.
• Highly expressive normalizing flow models enable accurate calculations of nuclear free energy and its derivatives.
• A single trained model can efficiently compute integrals for varied temperatures, densities, and nuclear forces.

Conclusions:

• Normalizing flows are a well-suited and powerful tool for high-dimensional integration in quantum many-body physics.
• This approach facilitates the development of accurate microscopic equations of state for astrophysical simulations.
• The method supports the integration of advanced nuclear forces and many-body techniques in future research.