I will discuss applications of deep neural networks as approximators. I will demonstrate an implementation of Gaussian processes for predicting baryon operator masses based on the meson spectrum of QCD, inspired by an idea from Witten. I will compare these results with those obtained from neural networks with finite width and depth. The second part of the talk will focus on using Physics-Informed Neural Networks (PINNs) to solve the Monge-Ampère equation on a Calabi-Yau manifold, including a comparison with approaches like Donaldson’s algorithm.

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