Machine Learning for Calabi-Yau metrics
Fabian Ruehle, CERN and Oxford, 12:00 ETAbstract:
String theory is a very promising candidate for a fundamental theory of our universe. An interesting prediction of string theory is that spacetime is ten-dimensional. Since we only observe four spacetime dimensions, the extra six dimensions are small and compact, thus evading detection.
These extra six-dimensional spaces, known as Calabi-Yau spaces, are very special and elusive. They come with a specific type of metric needed to make string theory consistent. While we know, thanks to the heroic work of Calabi and Yau, that this metric exists, we neither know what it looks like nor how to construct it explicitly.
Thinking of the metric as a function that satisfies three constraints entering the Calabi-Yau theorem, we can parameterize the metric as a neural network and formulate the problem as multiple continuous optimization tasks. I will show that this allows us to approximate Calabi-Yau metrics to very high accuracy, which will have important applications in Physics and Mathematics.