Quantum field theory on the computer
If you make the calculation grid increasingly finer, what happens to the result?
Image Credit: © TU Wien
Scientific Frontline: "At a Glance" Summary
- Main Discovery: Researchers successfully utilized Artificial Intelligence to solve a long-standing problem in particle physics: calculating Quantum Field Theories (QFT) on a lattice with optimal precision.
- Methodology: The team employed a specialized neural network architecture called "Lattice Gauge Equivariant Convolutional Neural Networks" (L-CNNs) to learn a "Fixed Point Action." This mathematical formulation allows the physics of the continuum to be mapped perfectly onto a coarse discrete grid, eliminating typical discretization errors.
- Key Data: The AI-driven approach significantly overcomes the "Critical Slowing Down" phenomenon, a major computational bottleneck where the cost of simulation increases dramatically as the lattice is refined. The new method allows simulations on coarse lattices to yield results as precise as those from extremely fine lattices, making previously impossible calculations feasible.
- Significance: This breakthrough enables the reliable and efficient simulation of complex quantum systems, such as the quark-gluon plasma (the state of the universe shortly after the Big Bang) or the internal structure of atomic nuclei, which were previously too computationally expensive for even the world's most powerful supercomputers.
- Future Application: The technique will be applied to gain deeper insights into the early universe, simulate experiments in particle colliders (like the Large Hadron Collider) with higher fidelity, and potentially explore new physics beyond the Standard Model by allowing for more rigorous error quantification.
- Branch of Science: Theoretical Particle Physics, Lattice Field Theory, and Artificial Intelligence (Machine Learning).
- Additional Detail: By using L-CNNs, the researchers ensured that the neural networks respect the fundamental symmetries of the gauge theories (gauge invariance), which is critical for the physical validity of the simulations.
An old puzzle in particle physics has been solved: How can quantum field theories be best formulated on a lattice to optimally simulate them on a computer? The answer comes from AI.
Quantum field theories are the foundation of modern physics. They tell us how particles behave and how their interactions can be described. However, many complicated questions in particle physics cannot be answered simply with pen and paper, but only through extremely complex quantum field theory computer simulations.
This presents exceptionally complex problems: Quantum field theories can be formulated in different ways on a computer. In principle, all of them yield the same physical predictions – but in radically different ways. Some variants are computationally completely unusable, inaccurate, or inefficient, while others are surprisingly practical. For decades, researchers have been searching for an optimal way to embed quantum theories in computer simulations. Now, a team from TU Wien, together with teams from the USA and Switzerland, has shown that artificial intelligence can bring about tremendous progress in this area.
In the computer, the whole world is a grid
"If we want to work with quantum field theories on a computer, we have to discretize them. That's nothing unusual," says David Müller from the Institute for Theoretical Physics at TU Wien. Every image on a computer screen consists of small, discrete pixels; when calculating the trajectory of a lunar rocket, the calculation is performed in small, discrete time steps.
It's the same in particle physics: A four-dimensional lattice is created, with three spatial dimensions and one-time dimensions. Each lattice point is stored on the computer, and the quantum field theory dictates how the lattice points influence each other. In this way, it is possible to simulate, for example, what happens during massive particle collisions at CERN, or how matter behaved shortly after the Big Bang. In quantum field theory, space and time are continuous. When mapping the theories onto a discrete lattice, however, one has certain degrees of freedom: Different lattice theories correspond to the same continuous theory. One must select a variant that promises the greatest computational success. If this is not done, the computer simulation may run into a dead end and fail to find the correct solution within a realistic timeframe.
Different scale, same result
An important key to success are so-called fixed-point equations. "There are certain formulations of quantum field theory on a lattice that have a particularly nice property," explains Urs Wenger from the University of Bern. "They ensure that certain properties remain the same, even if we make the lattice coarser or finer. If this is the case, we know: This property is reliable; it also agrees at coarse resolution – i.e., on a wide-mesh grid – with the continuum that would correspond to an infinitely fine grid."
It's a bit like a map that exists on different scales: Not all details will be the same on every version of the map. But some things don't change when the scale changes – for example, which country borders which other country. This means that one can be quite sure that this property, if it is independent of the map scale, is also a property of reality itself.
The success of AI
Even 30 years ago, experiments were conducted to adapt the lattice formulas in this way. However, there are hundreds of thousands of parameters – far too many for a human. "Many people began exploring these concepts three decades ago, but back then, we simply didn't have the technical means," says Kieran Holland from the University of the Pacific. "By joining forces with the team at TU Wien, we were finally able to revisit these long-standing ideas."
To turn this vision into reality, the team has now developed a very special neural network specifically for this purpose. Ready-made AI solutions do not lead to the goal; it was necessary to develop artificial intelligence that, from the outset, guarantees compliance with the physical laws that are specified.
The team has now succeeded in doing this. The result of the work: The action – the crucial physical quantity in such quantum field theories, also known from Planck's ‘quantum of action’– could be parameterized on a lattice using AI in such a way that even coarse lattices yield remarkably small errors. "We were able to show that this approach opens up a completely new way to simulate complex quantum field theories with manageable computational effort," says Andreas Ipp from TU Wien.
Resource material: The Physics of A.I. (YouTube)
Published in journal: Physical Review Letters
Title: Machine-Learned Renormalization-Group-Improved Gauge Actions and Classically Perfect Gradient Flows
Authors: Kieran Holland, Andreas Ipp, David I. Müller, and Urs Wenger
Source/Credit: Technische Universität Wien
Reference Number: phy012626_01
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