AI Boosts Nuclear Physics Calculations for Stars

Scientists are tackling the complex challenge of understanding atomic nuclei and neutron stars by modelling the interactions of protons and neutrons. Alessandro Lovato from Argonne National Laboratory, INFN-TIFPA Trento Institute of Fundamental Physics and Applications, and Instituto de Física Corpuscular (IFIC), alongside Giuseppe Carleo of the Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), and Bryce Fore from Argonne National Laboratory, lead a collaborative effort involving researchers at the University of Oslo, Ohio University, Universitat de Barcelona (UB) and Institut de Ciències del Cosmos, Fermi National Accelerator Laboratory, and the Instituto de Física Corpuscular (IFIC). Their work demonstrates the significant advancement offered by artificial neural networks in representing nuclear many-body wave functions, extending the reach of continuum quantum Monte Carlo methods. This innovative approach allows for calculations on larger systems and provides a versatile framework for investigating phenomena like nuclear clustering and superfluidity, ultimately paving the way for more unified and accurate descriptions of nuclear structure and reactions.

This innovative technique allows for unprecedentedly accurate modelling of atomic nuclei, unlocking insights into the heart of matter and the extreme environments within neutron stars. Understanding these fundamental building blocks promises to reshape our understanding of the universe.

Scientists have achieved a significant advance in modelling the structure of atomic nuclei and, by extension, neutron stars, through the innovative application of artificial neural networks. This work demonstrates that representing the complex wave function of atomic nuclei with these networks substantially improves the accuracy and scale of calculations performed using quantum Monte Carlo methods.

Previously, simulating the behaviour of these systems presented considerable computational challenges, limiting the size and complexity of nuclei that could be accurately modelled. Now, researchers have unlocked the potential to study larger, more intricate nuclear systems with unprecedented precision. The study centres on a novel approach to approximating the many-body wave function, a mathematical description of the quantum state of a system with multiple interacting particles.

By employing artificial neural networks, the team created a flexible and efficient means of representing this wave function, allowing for more accurate solutions to the Schrödinger equation. This breakthrough enables a deeper understanding of the forces governing nuclear interactions and the properties of nuclear matter under extreme conditions. Various wave function ansätze, including Pfaffian, Jastrow and Backflow correlations, were explored and refined to optimise the accuracy of the simulations.

A key accomplishment of this research is the successful application of these methods to calculate the properties of increasingly complex nuclei, culminating in simulations of oxygen-16. This represents a significant step forward, as heavier nuclei pose a far greater computational challenge than lighter ones. The ability to accurately model oxygen-16 validates the approach and paves the way for studying even heavier elements and exotic nuclear structures.

Furthermore, the techniques developed in this study have implications beyond nuclear physics, offering potential benefits to other areas of physics dealing with many-body quantum systems, such as condensed matter physics and ultra-cold Fermi gases. The researchers utilised quantum Monte Carlo methods, a class of computational algorithms that rely on random sampling to solve quantum mechanical problems. This work promises to unlock new insights into the behaviour of matter at the most fundamental level and has the potential to reshape our understanding of the universe.

Neural network modelling accurately predicts properties of Oxygen-16 nuclei

Calculations extending to Oxygen-16 (¹⁶O) have been successfully completed using artificial neural networks to model the wave function of atomic nuclei. This demonstrates the capability to accurately model systems with a mass number of 16, a complexity previously challenging for many computational methods. The research leverages neural network quantum states within continuum quantum Monte Carlo methods, enabling calculations across a wider range of length scales and density regimes than previously attainable.

The study explored various “wave function ansätze”, including Pfaffian-Jastrow and Backflow correlations, to refine the accuracy of the calculations. These advanced techniques allow for a more nuanced representation of the complex interactions between protons and neutrons within the nucleus. By incorporating these correlations, the model achieves a higher fidelity in predicting nuclear properties.

A key achievement of this work is the ability to accurately capture both continuous spatial coordinates and discrete spin, isospin degrees of freedom. This is crucial for modelling the intricate quantum behaviour of nucleons within the nucleus. The use of first-quantized neural network architectures, acting directly on these coordinates, offers a promising path toward overcoming limitations imposed by traditional basis truncations and the sign problem in quantum Monte Carlo simulations.

The nuclear Hamiltonian employed in the calculations incorporates leading-order pionless effective field theory, utilising contact interactions regularized with Gaussian cutoff functions. Specifically, the cutoff radii were set to R0 = 1.5459 fm and R1 = 1.8304 fm, with low-energy constants C01 = −5.27518671 fm² and C10 = −7.04040080 fm². These parameters were carefully adjusted to reproduce neutron, proton scattering data, ensuring the model’s consistency with experimental observations.

Deep learning of many-body wave functions for quantum Monte Carlo calculations

Artificial neural networks now serve as the core of a novel approach to modelling the wave function of atomic nuclei. This methodology leverages the power of deep learning to represent the complex many-body quantum states that describe the behaviour of protons and neutrons within the nucleus. Crucially, this allows for a significant expansion in the scale and accuracy of calculations performed using quantum Monte Carlo methods.

The research circumvents limitations of traditional methods by employing neural networks to approximate the wave function, enabling the study of larger and more intricate nuclear systems than previously feasible. Initial steps involved careful consideration of the “wave function ansatz”, or the mathematical form used to approximate the true wave function.

Several options were explored, including the established Slater-Jastrow approach, which combines a single-particle description with a correlation factor to account for interactions. Further refinements incorporated operator-dependent Slater-Jastrow forms and “hidden nucleons”, a technique that introduces auxiliary particles to improve the flexibility of the wave function.

These advancements aimed to capture the subtle correlations between nucleons that govern nuclear stability and properties. To enhance accuracy still further, the study implemented Pfaffian-Jastrow and Backflow correlations, driven by their ability to accurately represent strong correlations in nuclear systems. Optimisation strategies were then employed to train the neural networks, adjusting their parameters to minimise the energy of the system and converge towards the most accurate representation of the wave function.

Neural networks unlock accurate simulations of atomic nuclei up to Oxygen-16

Scientists are increasingly turning to artificial intelligence to tackle problems previously considered intractable in nuclear physics. The ability to accurately model the behaviour of protons and neutrons within atomic nuclei has long been hampered by computational limitations, a challenge now being addressed by the innovative application of artificial neural networks.

For decades, researchers have struggled to scale quantum Monte Carlo calculations to sufficiently complex systems, hindering progress in understanding the fundamental forces governing matter at its most dense. This new approach represents a significant leap forward, allowing for calculations on nuclei as large as Oxygen-16, a crucial milestone in the field.

What makes this work notable is not simply the increased scale of the calculations, but the method itself. By employing neural networks to represent the complex wave functions describing nuclear structure, scientists have created a more flexible and efficient means of approximating solutions to the notoriously difficult many-body problem. This isn’t merely about refining existing models; it’s about opening up entirely new avenues for exploring the behaviour of matter under extreme conditions, such as those found within neutron stars.

However, the path ahead is not without its obstacles. While the current study demonstrates success with Oxygen-16, extending these methods to even heavier nuclei will demand further algorithmic improvements and computational resources. Moreover, the choice of neural network architecture and the specific “wave function ansatz” remains a critical area of investigation.

Future work will likely focus on developing more robust and adaptable neural network designs, potentially incorporating techniques from other areas of machine learning. Ultimately, this research signals a broader shift in nuclear physics, one where the power of artificial intelligence is harnessed to unlock the secrets of the universe’s building blocks.