Machine learning Calabi-Yau metrics
This work addresses the computational bottleneck in physics and mathematics for simulating Calabi-Yau metrics, though it is incremental as it builds on existing methods.
The researchers tackled the problem of numerically approximating Calabi-Yau metrics by combining machine learning with Donaldson's algorithm, achieving a speedup of one to two orders of magnitude in computation time.
We apply machine learning to the problem of finding numerical Calabi-Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on Kähler manifolds, we combine conventional curve fitting and machine-learning techniques to numerically approximate Ricci-flat metrics. We show that machine learning is able to predict the Calabi-Yau metric and quantities associated with it, such as its determinant, having seen only a small sample of training data. Using this in conjunction with a straightforward curve fitting routine, we demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with our new machine-learning algorithm decreasing the time required by between one and two orders of magnitude.