A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.
Gravitational Duals from Equations of State
4 Pith papers cite this work, alongside 11 external citations. Polarity classification is still indexing.
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abstract
Holography relates gravitational theories in five dimensions to four-dimensional quantum field theories in flat space. Under this map, the equation of state of the field theory is encoded in the black hole solutions of the gravitational theory. Solving the five-dimensional Einstein's equations to determine the equation of state is an algorithmic, direct problem. Determining the gravitational theory that gives rise to a prescribed equation of state is a much more challenging, inverse problem. We present a novel approach to solve this problem based on physics-informed neural networks. The resulting algorithm is not only data-driven but also informed by the physics of the Einstein's equations. We successfully apply it to theories with crossovers, first- and second-order phase transitions.
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Extends PINN-based holographic inverse problem solving to false vacuum and large hierarchy regimes, claiming accurate scalar potential reconstruction from thermodynamic data despite numerical stiffness.
Density-of-states lattice study of the first-order phase transition in Sp(4) Yang-Mills theory at finite temperature, confirming metastability and surface tension for two temporal extents toward the continuum limit.
citing papers explorer
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Physics-Informed Neural Embeddings of PDE Solution Families
A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.
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Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua
Extends PINN-based holographic inverse problem solving to false vacuum and large hierarchy regimes, claiming accurate scalar potential reconstruction from thermodynamic data despite numerical stiffness.
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Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit
Density-of-states lattice study of the first-order phase transition in Sp(4) Yang-Mills theory at finite temperature, confirming metastability and surface tension for two temporal extents toward the continuum limit.
- Bound states and deconfinement from Romans supergravity with magnetic flux