Deep-Learning the Landscape
This provides a valuable tool for researchers in mathematical physics and pure mathematics to handle large-scale data, though it is incremental as it applies existing deep learning methods to new domains.
The authors tackled the problem of analyzing complex mathematical physics databases by applying deep learning to classify and predict quantities in areas like Calabi-Yau manifolds and gauge theories, finding that simple neural networks achieved high accuracy quickly and could predict new results.
We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete examples, we establish multi-layer neural networks as both classifiers and predictors and train them with a host of available data ranging from Calabi-Yau manifolds and vector bundles, to quiver representations for gauge theories. We find that even a relatively simple neural network can learn many significant quantities to astounding accuracy in a matter of minutes and can also predict hithertofore unencountered results. This paradigm should prove a valuable tool in various investigations in landscapes in physics as well as pure mathematics.