Markus Rummel

Yang-Hui He, Dhagash Mehta, Matthew Niemerg et al.

Solving large polynomial systems with coefficient parameters are ubiquitous and constitute an important class of problems. We demonstrate the computational power of two methods--a symbolic one called the Comprehensive Gröbner basis and a numerical one called the cheater's homotopy-applied to studying both potential energy landscapes and a variety of questions arising from geometry and phenomenology. Particular attention is paid to an example in flux compactification where important physical quantities such as the gravitino and moduli masses and the string coupling can be efficiently extracted.

Zakaria Patel, Markus Rummel

Neural networks allow us to model complex relationships between variables. We show how to efficiently find extrema of a trained neural network in regression problems. Finding the extremizing input of an approximated model is formulated as the training of an additional neural network with a loss function that minimizes when the extremizing input is achieved. We further show how to incorporate additional constraints on the input vector such as limiting the extrapolation of the extremizing input vector from the original training data set. An instructional example of this approach using TensorFlow is included.