9 papers
Black Hole Black Boxes: Numerical Black Hole Metrics via AInstein Neural Networks
Tancredi Schettini Gherardini, Edward Hirst, Alexander George Stapleton
The AInstein architecture introduced an unsupervised neural method for solving the Riemannian Einstein equations on arbitrary manifolds. This Physics Informed Neural Network approa…
PINNs in More General Geometry
Edward Hirst
Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minim…
Minimising Willmore Energy via Neural Flow
Edward Hirst, Henrique N. Sá Earp, Tomás S. R. Silva
The neural Willmore flow of a closed oriented -surface in is introduced as a natural evolution process to minimise the Willmore energy, which is the squared …
Versor: A Geometric Sequence Architecture
Truong Minh Huy, Edward Hirst
A novel sequence architecture is introduced, Versor, which uses Conformal Geometric Algebra (CGA) in place of traditional linear operations to achieve structural generalization and…
A Machine Learning Approach to the Nirenberg Problem
Gianfranco Cortés, Maria Esteban-Casadevall, Yueqing Feng +4
This work introduces the Nirenberg Neural Network: a numerical approach to the Nirenberg problem of prescribing Gaussian curvature on for metrics that are pointwise conformal…
Approximate Gaussianity Beyond Initialisation in Neural Networks
Edward Hirst, Sanjaye Ramgoolam
Ensembles of neural network weight matrices are studied through the training process for the MNIST classification problem, testing the efficacy of matrix models for representing th…