Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua

David Mateos; Pablo Tejerina-P\'erez; Pau Sol\'e-Vilar\'o; Pavlos Protopapas; Pedro Taranc\'on-\'Alvarez; Raul Jimenez

arxiv: 2606.30117 · v1 · pith:J6H27RN5new · submitted 2026-06-29 · ✦ hep-th · astro-ph.CO· cs.AI· cs.LG· gr-qc

Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua

Raul Jimenez , David Mateos , Pavlos Protopapas , Pau Sol\'e-Vilar\'o , Pedro Taranc\'on-\'Alvarez , Pablo Tejerina-P\'erez This is my paper

Pith reviewed 2026-06-30 05:00 UTC · model grok-4.3

classification ✦ hep-th astro-ph.COcs.AIcs.LGgr-qc

keywords holographic dualityphysics-informed neural networksscalar potential reconstructionfalse vacuarenormalization group flowsthermodynamic datagauge/gravity dualitylarge hierarchies

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The pith

Improved PINNs reconstruct bulk scalar potentials from thermodynamic data deep into false vacuum regimes with large hierarchies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends a Physics-Informed Neural Network method to solve the holographic inverse problem of recovering the bulk scalar potential from boundary thermodynamic data. It targets regimes with false vacua and large energy scale hierarchies that produce near-degenerate states, stiff numerics, and regions of the potential left unprobed by the input data. The authors introduce methodological advances that overcome these issues and demonstrate accurate recovery of the potential, including its false-vacuum features, with good agreement to the underlying thermodynamics. A sympathetic reader would care because this enlarges the range of strongly coupled quantum field theories whose gravitational duals can be inferred from observable data, including those with exotic renormalization group flows that skip between non-adjacent fixed points.

Core claim

An improved PINNs framework can accurately reconstruct scalar potentials deep into the false vacuum regime, achieving robust agreement with the physical features of the underlying thermodynamics despite significant numerical stiffness and unprobed regions of the potential.

What carries the argument

Physics-Informed Neural Networks (PINNs) extended with new training strategies that handle near-degenerate states, large energy hierarchies, and input data that leaves parts of the potential unprobed.

If this is right

Holographic models with skipping RG flows between non-adjacent fixed points become accessible to data-driven reconstruction.
Thermodynamic data from strongly coupled theories with large scale hierarchies can be inverted to obtain the dual geometry even when the potential is only partially sampled.
The same numerical advances apply to other holographic inverse problems that suffer from stiffness or incomplete data coverage.
Machine-learning methods can now probe exotic thermodynamic phases that were previously unreachable by direct reconstruction techniques.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could be tested on lattice or experimental thermodynamic data from real materials or cold-atom systems that exhibit metastable phases.
Similar PINN adaptations might solve inverse problems in other gravity-matter systems where the potential is not fully constrained by boundary observables.
If the reconstruction remains stable under noise in the input data, it would open a route to inferring dual geometries from noisy experimental measurements.

Load-bearing premise

The input thermodynamic data still contains enough information to recover the full potential, including false-vacuum features, even when some regions remain unprobed.

What would settle it

Take a known holographic model with a false vacuum, generate its thermodynamic data, run the improved PINN reconstruction, and check whether the output potential reproduces the correct thermodynamics in the false-vacuum region to within numerical tolerance.

read the original abstract

We investigate the reconstruction of holographic duals for strongly coupled quantum field theories in regimes characterized by large hierarchies and the presence of false vacua. Within the gauge/gravity duality, these features translate into non-trivial thermodynamic behaviour and exotic renormalization group flows, including skipping flows between non-adjacent fixed points. Building on previous work based on Physics-Informed Neural Networks (PINNs), we extend the holographic inverse problem of reconstructing the bulk scalar potential from boundary thermodynamic data into this new regime. This setting presents a variety of conceptual and numerical challenges, such as near-degenerate states, large hierarchies of energy scales, and regions of the potential that are not directly probed by the input data. We develop a set of methodological advances that overcome these obstacles, thereby improving the established PINNs-based methodology and extending it to new physical regimes of interest that were previously out of reach. Applying the developed framework, we demonstrate accurate reconstruction of scalar potentials deep into the false vacuum regime, achieving robust agreement with the physical features of the underlying thermodynamics despite significant numerical stiffness. Our results extend the bridge between holography and machine learning, and suggest that data-driven approaches can provide new insights into the structure of strongly coupled systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Extends prior PINN work on holographic potential reconstruction into false vacua and large hierarchies, with claimed robustness to stiffness.

read the letter

The paper takes the existing PINN framework for inverting boundary thermodynamics into bulk scalar potentials and adapts it for regimes with false vacua, skipping RG flows, and big scale separations. The main contribution is a set of training adjustments that let the network handle numerical stiffness and regions of the potential not directly constrained by the input data.

They identify the concrete obstacles—near-degenerate states, unprobed potential segments, and hierarchy-induced stiffness—and report that the modified approach recovers potentials whose thermodynamics match the input even deep in the false vacuum. This is a straightforward extension rather than a new architecture, but it targets regimes that were previously out of reach for the method.

The soft spot is that the abstract supplies no error bars, no ablation on the new loss terms, and no explicit test that the reconstruction in unprobed regions is determined by the data rather than by network bias. Without those checks it is hard to judge how much the agreement relies on the physical features versus the regularization. The central assumption—that thermodynamic data still encodes enough information for the full potential including false-vacuum structure—needs stronger verification than is shown here.

The work is aimed at the small group already combining holography with machine learning for strongly coupled systems. A reader in that niche can extract practical implementation ideas. It is coherent on its own terms and the claims are specific enough to be checked, so it deserves a serious referee even if revisions will be needed on the validation side.

Referee Report

0 major / 0 minor

Summary. The manuscript extends PINN-based reconstruction of bulk scalar potentials from boundary thermodynamic data to holographic models featuring large energy hierarchies and false vacua. It introduces methodological advances to address numerical stiffness, near-degenerate states, and regions of the potential unprobed by input data, claiming accurate recovery of the potential including false-vacuum features and agreement with underlying thermodynamics.

Significance. If the reconstruction procedure is robust, the work would meaningfully broaden the scope of data-driven holographic methods to previously inaccessible regimes involving exotic RG flows and false vacua, strengthening the interface between machine learning and gauge/gravity duality.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their review and for acknowledging the potential of our extension of PINN-based holographic reconstruction to regimes with large energy hierarchies and false vacua. The manuscript demonstrates that the developed methodological advances overcome the associated numerical stiffness and allow accurate recovery of the scalar potential, including false-vacuum features, with robust agreement to the input thermodynamics. Since the report lists no specific major comments, we have no point-by-point responses to provide at this stage.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper extends a PINN-based inverse reconstruction of bulk scalar potentials from boundary thermodynamic data into regimes with false vacua and large hierarchies. The abstract and description frame this as a data-driven recovery that overcomes numerical stiffness via methodological advances, with the central claim being agreement between recovered potentials and input thermodynamics. No equations, loss functions, or derivation steps are exhibited that reduce the output potential to a fitted input by construction, nor is there a load-bearing self-citation chain that imports uniqueness or ansatz without independent verification. The reconstruction is presented as solving an inverse problem against external thermodynamic benchmarks rather than a tautology or renamed known result. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No details available from abstract alone on free parameters, axioms, or invented entities used in the reconstruction.

pith-pipeline@v0.9.1-grok · 5785 in / 998 out tokens · 51039 ms · 2026-06-30T05:00:07.037514+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

26 extracted references · 11 canonical work pages · 4 internal anchors

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work page arXiv 2024
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Taranc´ on-´Alvarez, P

P. Taranc´ on-´Alvarez, P. Tejerina-P´ erez, R. Jimenez and P. Protopapas,Efficient pinns via multi-head unimodular regularization of the solutions space,Communications Physics8 (2025) 335

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J. Sirignano and K. Spiliopoulos,Dgm: A deep learning algorithm for solving partial differential equations,Journal of Computational Physics375(2018) 1339

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The Large N Limit of Superconformal Field Theories and Supergravity

J.M. Maldacena,The Large N limit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231 [hep-th/9711200]

work page internal anchor Pith review Pith/arXiv arXiv 1998

[2] [2]

Gauge Theory Correlators from Non-Critical String Theory

S.S. Gubser, I.R. Klebanov and A.M. Polyakov,Gauge theory correlators from noncritical string theory,Phys. Lett. B428(1998) 105 [hep-th/9802109]

work page internal anchor Pith review Pith/arXiv arXiv 1998

[3] [3]

Anti De Sitter Space And Holography

E. Witten,Anti-de Sitter space and holography,Adv. Theor. Math. Phys.2(1998) 253 [hep-th/9802150]

work page internal anchor Pith review Pith/arXiv arXiv 1998

[4] [4]

Aharony, S.S

O. Aharony, S.S. Gubser, J. Maldacena, H. Ooguri and Y. Oz,Large n field theories, string theory and gravity,Physics Reports323(2000) 183

2000

[5] [5]

Y. Bea, R. Jimenez, D. Mateos, S. Liu, P. Protopapas, P. Taranc´ on-´Alvarez et al., Gravitational duals from equations of state,JHEP07(2024) 087 [2403.14763]

work page arXiv 2024

[6] [6]

Taranc´ on-´Alvarez, P

P. Taranc´ on-´Alvarez, P. Tejerina-P´ erez, R. Jimenez and P. Protopapas,Efficient pinns via multi-head unimodular regularization of the solutions space,Communications Physics8 (2025) 335

2025

[7] [7]

Bea and D

Y. Bea and D. Mateos,Heating up exotic rg flows with holography,Journal of High Energy Physics2018(2018) 1

2018

[8] [8]

Kiritsis, F

E. Kiritsis, F. Nitti and L. Silva Pimenta,Exotic rg flows from holography,Fortschritte der Physik65(2017) 1600120

2017

[9] [9]

Hairer and G

E. Hairer and G. Wanner,Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, vol. 14 (01, 1996), 10.1007/978-3-662-09947-6

work page doi:10.1007/978-3-662-09947-6 1996

[10] [10]

Seiler, W

E. Seiler, W. Lei and P. Protopapas,Stiff transfer learning for physics-informed neural networks,

[11] [11]

De Boer, E

J. De Boer, E. Verlinde and H. Verlinde,On the holographic renormalization group,Journal of High Energy Physics2000(2000) 003

2000

[12] [12]

Kiritsis, W

E. Kiritsis, W. Li and F. Nitti,Holographic rg flow and the quantum effective action, Fortschritte der Physik62(2014) 389

2014

[13] [13]

Dissanayake and N

M. Dissanayake and N. Phan-Thien,Neural-network-based approximations for solving partial differential equations,communications in Numerical Methods in Engineering10(1994) 195

1994

[14] [14]

Lagaris, A

I. Lagaris, A. Likas and D. Fotiadis,Artificial neural networks for solving ordinary and partial differential equations,IEEE Transactions on Neural Networks9(1998) 987

1998

[15] [15]

Lagaris, A

I. Lagaris, A. Likas and D. Papageorgiou,Neural-network methods for boundary value problems with irregular boundaries,IEEE Transactions on Neural Networks11(2000) 1041

2000

[16] [16]

Raissi, P

M. Raissi, P. Perdikaris and G. Karniadakis,Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,Journal of Computational Physics378(2019) 686. – 32 –

2019

[17] [17]

Mattheakis, D

M. Mattheakis, D. Sondak, A.S. Dogra and P. Protopapas,Hamiltonian neural networks for solving equations of motion,Phys. Rev. E105(2022) 065305

2022

[18] [18]

Sirignano and K

J. Sirignano and K. Spiliopoulos,Dgm: A deep learning algorithm for solving partial differential equations,Journal of Computational Physics375(2018) 1339

2018

[19] [19]

Y. Zhu, N. Zabaras, L. Lu and P. Perdikaris,Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data, Journal of Computational Physics394(2019) 56

2019

[20] [20]

Choudhary, J.F

A. Choudhary, J.F. Lindner, E.G. Holliday, S.T. Miller, S. Sinha and W.L. Ditto,Physics enhanced neural networks predict order and chaos,Phys. Rev. E 101, 062207 (2020)101 (2019) 062207 [1912.01958]

work page arXiv 2020

[21] [21]

Choudhary, J.F

A. Choudhary, J.F. Lindner, E.G. Holliday, S.T. Miller, S. Sinha and W.L. Ditto,Forecasting hamiltonian dynamics without canonical coordinates,2010.15201

work page arXiv 2010

[22] [22]

CoRR , volume =

S. Greydanus, M. Dzamba and J. Yosinski,Hamiltonian neural networks,1906.01563

work page arXiv 1906

[23] [23]

Flamant, P

C. Flamant, P. Protopapas and D. Sondak,Solving differential equations using neural network solution bundles,arXiv preprint arXiv:2006.14372(2020)

work page arXiv 2006

[24] [24]

Attems, J

M. Attems, J. Casalderrey-Solana, D. Mateos, I. Papadimitriou, D. Santos-Oliv´ an, C.F. Sopuerta et al.,Thermodynamics, transport and relaxation in non-conformal theories, Journal of High Energy Physics2016(2016) 1

2016

[25] [25]

Holographic Collisions in Non-conformal Theories

M. Attems, J. Casalderrey-Solana, D. Mateos, D. Santos-Oliv´ an, C.F. Sopuerta, M. Triana et al.,Holographic Collisions in Non-conformal Theories,JHEP01(2017) 026 [1604.06439]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[26] [26]

Casalderrey-Solana, L

J. Casalderrey-Solana, L. Castells-Tiestos, J. Gon¸ calves and D. Mateos,Self-sustained, out-of-equilibrium inflation,2512.18079. – 33 –

work page arXiv