Title:

Calculating Ricci-flat Metrics for Calabi-Yau Manifolds with Machine Learning

String theory seeks to explain gravity, electromagnetism, and the weak and strong nuclear forces in one theory, arguing that in addition to the four known dimensions, there are six additional dimensions. Curled-up six-dimensional Calabi-Yau (CY) manifolds show the geometry of the extra dimensions, and they have a strong effect on the properties of the four-dimensional universe. Computing the Ricci-flat metric with the Monge-Ampere equation is necessary to determine whether a given CY geometry is realistic for our universe. Machine learning techniques are very useful to solve the Monge-Ampère equation. Previous work has focused on using Multi-Layer Perceptrons, a type of neural network with weights on the nodes and activation functions. We used TensorFlow Dense networks and implemented Fourier features and adaptive Fourier features, which capture high frequency areas of the CY manifold, particularly in deformed manifolds. The adaptive Fourier features have an additional dense network inside of them to apply them as needed throughout the CY manifold. The adaptive Fourier features perform the best, and the Fourier features are the worst, with the dense network being in between.

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