Multi-lattice sampling of quantum field theories via neural operator-based flows
We consider the problem of sampling lattice field configurations on a lattice from the Boltzmann distribution corresponding to some action. Since such densities arise as approximationw of an underlying functional density, we frame the task as an instance of operator learning. We propose to approxima...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2024-01-01
|
| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/ad9707 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846141308155985920 |
|---|---|
| author | Bálint Máté François Fleuret |
| author_facet | Bálint Máté François Fleuret |
| author_sort | Bálint Máté |
| collection | DOAJ |
| description | We consider the problem of sampling lattice field configurations on a lattice from the Boltzmann distribution corresponding to some action. Since such densities arise as approximationw of an underlying functional density, we frame the task as an instance of operator learning. We propose to approximate a time-dependent neural operator whose time integral provides a mapping between the functional distributions of the free and target theories. Once a particular lattice is chosen, the neural operator can be discretized to a finite-dimensional, time-dependent vector field which in turn induces a continuous normalizing flow between finite dimensional distributions over the chosen lattice. This flow can then be trained to be a diffeormorphism between the discretized free and target theories on the chosen lattice, and, by construction, can be evaluated on different discretizations of spacetime. We experimentally validate the proposal on the 2-dimensional φ ^4 -theory to explore to what extent such operator-based flow architectures generalize to lattice sizes they were not trained on, and show that pretraining on smaller lattices can lead to a speedup over training directly on the target lattice size. |
| format | Article |
| id | doaj-art-4f8ff28da1d64c65b639cc12c2d3c60a |
| institution | Kabale University |
| issn | 2632-2153 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-4f8ff28da1d64c65b639cc12c2d3c60a2024-12-04T12:46:36ZengIOP PublishingMachine Learning: Science and Technology2632-21532024-01-015404505310.1088/2632-2153/ad9707Multi-lattice sampling of quantum field theories via neural operator-based flowsBálint Máté0https://orcid.org/0000-0001-9144-9206François Fleuret1Department of Computer Science, University of Geneva , Geneva, SwitzerlandDepartment of Computer Science, University of Geneva , Geneva, SwitzerlandWe consider the problem of sampling lattice field configurations on a lattice from the Boltzmann distribution corresponding to some action. Since such densities arise as approximationw of an underlying functional density, we frame the task as an instance of operator learning. We propose to approximate a time-dependent neural operator whose time integral provides a mapping between the functional distributions of the free and target theories. Once a particular lattice is chosen, the neural operator can be discretized to a finite-dimensional, time-dependent vector field which in turn induces a continuous normalizing flow between finite dimensional distributions over the chosen lattice. This flow can then be trained to be a diffeormorphism between the discretized free and target theories on the chosen lattice, and, by construction, can be evaluated on different discretizations of spacetime. We experimentally validate the proposal on the 2-dimensional φ ^4 -theory to explore to what extent such operator-based flow architectures generalize to lattice sizes they were not trained on, and show that pretraining on smaller lattices can lead to a speedup over training directly on the target lattice size.https://doi.org/10.1088/2632-2153/ad9707normalizing flowslattice field theoryneural operatorsflow-based sampling |
| spellingShingle | Bálint Máté François Fleuret Multi-lattice sampling of quantum field theories via neural operator-based flows Machine Learning: Science and Technology normalizing flows lattice field theory neural operators flow-based sampling |
| title | Multi-lattice sampling of quantum field theories via neural operator-based flows |
| title_full | Multi-lattice sampling of quantum field theories via neural operator-based flows |
| title_fullStr | Multi-lattice sampling of quantum field theories via neural operator-based flows |
| title_full_unstemmed | Multi-lattice sampling of quantum field theories via neural operator-based flows |
| title_short | Multi-lattice sampling of quantum field theories via neural operator-based flows |
| title_sort | multi lattice sampling of quantum field theories via neural operator based flows |
| topic | normalizing flows lattice field theory neural operators flow-based sampling |
| url | https://doi.org/10.1088/2632-2153/ad9707 |
| work_keys_str_mv | AT balintmate multilatticesamplingofquantumfieldtheoriesvianeuraloperatorbasedflows AT francoisfleuret multilatticesamplingofquantumfieldtheoriesvianeuraloperatorbasedflows |