Suresh Nampuri

Gabriel Lopes Cardoso, Damián Mayorga Peña, Suresh Nampuri

We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the presence of a potential for the neutral scalar fields. For a certain solution subspace, we demonstrate partial integrability by showing that a subset of the equations of motion in two dimensions are the compatibility conditions for a linear system. Subsequently, we study the integrability of these two-dimensional models from a complementary one-dimensional point of view, framed in terms of Liouville integrability. In this endeavour, we employ various machine learning techniques to systematise our search for numerical Lax pair matrices for these models, as well as conserved currents expressed as functions of phase space variables.

Vishnu Jejjala, Suresh Nampuri, Dumisani Nxumalo et al.

Modular, Jacobi, and mock-modular forms serve as generating functions for BPS black hole degeneracies. By training feed-forward neural networks on Fourier coefficients of automorphic forms derived from the Dedekind eta function, Eisenstein series, and Jacobi theta functions, we demonstrate that machine learning techniques can accurately predict modular weights from truncated expansions. Our results reveal strong performance for negative weight modular and quasi-modular forms, particularly those arising in exact black hole counting formulae, with lower accuracy for positive weights and more complicated combinations of Jacobi theta functions. This study establishes a proof of concept for using machine learning to identify how data is organized in terms of modular symmetries in gravitational systems and suggests a pathway toward automated detection and verification of symmetries in quantum gravity.