<div class="csl-bib-body">
<div class="csl-entry">Ranner, T. R., Ipp, A., & Müller, D. (2025, September 25). <i>Score-based diffusion models for lattice field theory</i> [Presentation]. International Artificial Intelligence Summer School, Castiglione della Pescaia, Italy. http://hdl.handle.net/20.500.12708/219895</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/219895
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dc.description.abstract
Score-based diffusion models are generative deep learning models that have been highly successful,
especially in the field of image generation. While they are inspired by a physical process,
the diffusion, they were not designed with applications in physics in mind. However, recently
their potential for application in theoretical physics, specifically in lattice field theory, has been
demonstrated.
Lattice field theory (LFT) is a numerical tool which is essential for many numerical calculations
in quantum field theory (QFT). Quantum field theory is the framework in which the standard
model of particle physics is formulated, which is our current best understanding of the fundamental
particles and interactions (except for gravity). For LFT, the fields of QFT are discretized in space
and time and put onto a lattice. Probability distributions of those discrete field configurations are
known, and to calculate physical observables of the field theory one has to sample a large number
of field configurations according to these distributions. This computationally very intensive task
is usually done with Monte Carlo methods. These face problems, especially when going to larger
lattices, which may make calculations intractable.
Inspired by the analogous data structures of two-dimensional lattices and images, one can
instead use modern image generation methods. Score-based diffusion models have recently been
successfully applied to scalar field theory, a theory with a single scalar degree of freedom
at each lattice site. In our work, we further investigated score-based diffusion models in the context
of scalar field theory and also applied them to U(1) lattice gauge theory.
We found that the results of the diffusion model for scalar field theory are almost perfect,
while for U(1) gauge theory there were some problems when going to a parameter regime of the
theory which is especially hard to sample from. Very recently, a group, with which we now also
collaborate, has found a workaround to this problem by introducing a new generative diffusion
process. It is based on the fact that the score (which is what the neural network
learns) in score-based diffusion models corresponds to the negative gradient of the action (an
important physical quantity describing the theory) of the LFT. We also used this correspondence
by integrating physical knowledge into the network design and were able to achieve a significant
speed-up of the training process. Furthermore, by adapting the diffusion model such that the
network learns not the gradient of the action, but the action itself, we were also able to decrease
the number of necessary training steps, though each training step became more costly. Still, as the
action is a quantity of interest in physics, this may have further applications. For example, one
could determine the action of an experimental system which is only accessible by measurements of
field configurations. Another avenue we started to explore is to use networks trained at a certain
lattice size to generate configurations on bigger lattices.
While the theories we studied until now can still be properly covered by traditional numerical
methods, we are confident that diffusion models have a huge potential in more involved theories.
In this spirit, we just started a collaboration where we aim to apply score-based diffusion models
to more complex non-abelian theories such as SU(2) gauge theory. We hope that the integration of
deep learning techniques will enable us to massively improve upon existing calculations in lattice
field theory.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
lattice field theory
en
dc.subject
diffusion model
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dc.subject
lattice gauge theory
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dc.title
Score-based diffusion models for lattice field theory
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
PAT3667424
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dc.type.category
Presentation
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tuw.project.title
Maschinelles Lernen mit Renormierungsgruppe für Gitter QCD
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tuw.researchTopic.id
C6
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tuw.researchTopic.name
Modeling and Simulation
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E136 - Institut für Theoretische Physik
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tuw.author.orcid
0000-0001-9511-3523
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tuw.author.orcid
0000-0002-8163-7614
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tuw.event.name
International Artificial Intelligence Summer School
