The Standard Model in particle physics encompasses all recognized elementary particles and explains three of the four fundamental forces that shape our universe, excluding gravity. These essential forces—electromagnetic, strong, and weak—determine particle formation, interactions, and eventual decay processes.
Researching particle and nuclear physics within this theoretical framework presents significant challenges, heavily depending on extensive numerical computations. For instance, understanding numerous aspects of the strong force demands numerical simulations at scales ranging from one-tenth to one-hundredth of a proton's size to address fundamental inquiries regarding proton, neutron, and nuclei characteristics.
“Ultimately, we face computational limitations when investigating proton and nuclear structure using lattice field theory,” explains physics assistant professor Phiala Shanahan. “Numerous fascinating problems exist that we theoretically understand how to solve, yet we lack sufficient computational resources, despite utilizing the world's most powerful supercomputers.”
To overcome these limitations, Shanahan leads a research group integrating theoretical physics with machine learning models. In their publication “Equivariant flow-based sampling for lattice gauge theory,” featured this month in Physical Review Letters, they demonstrate how incorporating physics theory symmetries into machine learning and artificial intelligence architectures can dramatically accelerate algorithms for theoretical physics research.
“We're employing machine learning not to analyze vast datasets, but to expedite first-principles theory without compromising methodological rigor,” Shanahan states. “This specific work proves we can construct machine learning architectures incorporating certain symmetries from the Standard Model of particle and nuclear physics, accelerating our targeted sampling problems by multiple orders of magnitude.”
Shanahan initiated the project alongside MIT graduate student Gurtej Kanwar and Michael Albergo, now at NYU. The project expanded to include Center for Theoretical Physics postdocs Daniel Hackett and Denis Boyda, NYU Professor Kyle Cranmer, and physics-knowledgeable machine-learning scientists from Google Deep Mind, Sébastien Racanière and Danilo Jimenez Rezende.
This month's paper represents one in a series aimed at enabling theoretical physics studies currently deemed computationally infeasible. “Our objective involves developing novel algorithms for a crucial component of numerical calculations in theoretical physics,” Kanwar explains. “These calculations illuminate the inner workings of the Standard Model of particle physics, our most fundamental theory of matter. Such calculations prove essential for comparing results from particle physics experiments, like the Large Hadron Collider at CERN, both to refine the model more precisely and to identify where the model fails and requires extension to something more fundamental.”
The only known systematically controllable method for studying the Standard Model of particle physics in the nonperturbative regime relies on sampling snapshots of quantum fluctuations in the vacuum. By measuring properties of these fluctuations, researchers can deduce characteristics of particles and collisions of interest.
This technique presents challenges, Kanwar notes. “This sampling process proves computationally expensive, and we seek to utilize physics-inspired machine learning techniques to generate samples far more efficiently,” he says. “Machine learning has already achieved remarkable progress in generating images, including recent work by NVIDIA to create facial images 'imagined' by neural networks. Viewing these vacuum snapshots as images, we find it natural to apply similar methodologies to our problem.”
Shanahan adds, “In our approach to sampling these quantum snapshots, we optimize a model that transitions from an easily sampleable space to the target space: once trained, sampling becomes efficient since you merely need to take independent samples in the easily sampleable space and transform them via the learned model.”
Specifically, the team has introduced a framework for constructing machine-learning models that precisely respect a category of symmetries, known as "gauge symmetries," essential for high-energy physics studies.
As a proof of concept, Shanahan and colleagues employed their framework to train machine-learning models simulating a two-dimensional theory, resulting in orders-of-magnitude efficiency improvements over cutting-edge techniques and more precise theoretical predictions. This breakthrough paves the way for significantly accelerated research into nature's fundamental forces using physics-informed machine learning.
The group's initial collaborative papers focused on applying machine-learning techniques to simple lattice field theory, developing these approaches on compact, connected manifolds describing the more complex field theories of the Standard Model. Now they're working to scale these techniques to state-of-the-art calculations.
“I believe we've demonstrated throughout the past year the tremendous potential in combining physics knowledge with machine learning techniques,” Kanwar remarks. “We're actively strategizing how to overcome remaining barriers preventing full-scale simulations using our approach. I hope to witness the first application of these methods to large-scale calculations within the next few years. If we successfully overcome the final obstacles, this promises to expand what we can achieve with limited resources, and I aspire to soon perform calculations that provide novel insights into what exists beyond our current understanding of physics.”
This concept of physics-informed machine learning is also termed “ab-initio AI” by the team, a central theme of the recently established MIT-based National Science Foundation Institute for Artificial Intelligence and Fundamental Interactions (IAIFI), where Shanahan serves as research coordinator for physics theory.
Led by the Laboratory for Nuclear Science, the IAIFI comprises both physics and AI researchers from MIT, Harvard, Northeastern, and Tufts universities.
“Our collaboration exemplifies the IAIFI spirit, with a diverse team uniting to simultaneously advance AI and physics” Shanahan states. Beyond research like Shanahan's focusing on physics theory, IAIFI researchers are also leveraging AI to enhance scientific potential at various facilities, including the Large Hadron Collider and the Laser Interferometer Gravity Wave Observatory, while simultaneously advancing AI itself.
