PINNs for N=2* holography
Abstract
Can a holographic theory be reconstructed from its equation of state? We investigate this question using physics-informed neural networks in the bosonic-mass sector of the Pilch--Warner model. We first validate the PINN approach against an analytic solution encoding the leading high-temperature corrections to the conformal equation of state. We then reconstruct nonlinear black-brane geometries and the scalar potential using thermodynamics, ultraviolet asymptotics, Ward identities, and horizon regularity. Independent solutions of the bulk Einstein-scalar equations demonstrate that accurately reproducing thermodynamics with a trained PINN does not guarantee an accurate reconstruction of the scalar potential. High-precision knowledge of the high-temperature equation of state constrains nonlinear interactions in the bulk scalar potential. Fixing the cubic coupling to its exact PW value, motivated by this high-temperature extraction, reduces the maximum sampled error in the reconstructed scalar self-interactions by a factor of ∼ 15 compared with constraining only the bulk scalar mass. Adding knowledge of the bulk viscosity of the gauge theory plasma further reduces this error by an additional factor of ∼ 13, with independent forward solutions reproducing the bulk viscosity within 0.09%.
Related
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- Accelerating natural gradient descent for PINNs with randomized numerical linear algebra
- An improved periodic activation for PINNs reconstructing convective flows
- A neural characteristic mapping method: Lagrangian PINNs based on flow maps for transport-dominated problems
- Staged Depth Training: A Representation Curriculum for PINNs
BibTeX
@misc{buchel2026pinns,
title = {{PINNs for N=2* holography}},
author = {Alex Buchel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14461},
eprint = {2610.14461},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14461},
}
RIS
TY - UNPB
TI - PINNs for N=2* holography
AU - Alex Buchel
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14461
UR - https://arxiv.org/abs/2610.14461
AB - Can a holographic theory be reconstructed from its equation of state? We investigate this question using physics-informed neural networks in the bosonic-mass sector of the Pilch--Warner model. We first validate the PINN approach against an analytic solution encoding the leading high-temperature corrections to the conformal equation of state. We then reconstruct nonlinear black-brane geometries and the scalar potential using thermodynamics, ultraviolet asymptotics, Ward identities, and horizon regularity. Independent solutions of the bulk Einstein-scalar equations demonstrate that accurately reproducing thermodynamics with a trained PINN does not guarantee an accurate reconstruction of the scalar potential. High-precision knowledge of the high-temperature equation of state constrains nonlinear interactions in the bulk scalar potential. Fixing the cubic coupling to its exact PW value, motivated by this high-temperature extraction, reduces the maximum sampled error in the reconstructed scalar self-interactions by a factor of ∼ 15 compared with constraining only the bulk scalar mass. Adding knowledge of the bulk viscosity of the gauge theory plasma further reduces this error by an additional factor of ∼ 13, with independent forward solutions reproducing the bulk viscosity within 0.09%.
ER -