SAIP2025

Laplacian eigenmodes in twisted periodic topologies for new physics models

Not scheduled

1h

Solomon Mahlangu House (University of the Witwatersrand, Johannesburg)

Oral Presentation Track G - Theoretical and Computational Physics Theoretical and Computational Physics

Speaker

Anele Ncube (University of Johannesburg)

Description

Laplacian eigenmodes in non-trivial topologies (e.g. having twisted periodicity) are important in constructing a complete picture of the physics at play within models that incorporate compact extradimensional spaces. Determining them analytically is generally unwieldy, and the existing standard numerical methods have limited ability as spatial dimensions increase and when computing higher-index eigenmodes is required. To determine the feasibility of using physics-informed neural networks to compute Laplacian eigenmodes, we apply them to three primitive test cases: the Möbius strip, the real projective plane ($\mathbb{R} P^2$) and the 3-torus ($T^3$) in Cartesian coordinates. The neural networks approach's potential performance beyond solving the simpler cases is estimated in terms of the approximation errors obtained by comparing with known analytical solutions.