A neural network surrogate model for scalar-Gauss-Bonnet black holes using gradient descent with a cyclical learning rate

Abstract The importance of machine learning in every area of science is quickly becoming apparent and gravitational physics is no exception. Keeping in mind the complexity of the field equations in different theories of gravitation, the approximating power of neural networks finds many applications. One such example is considered in this paper. We use a neural network surrogate model to approximate the relations between the mass M , the scalar charge D , and the radius of the horizon r H of a black hole in scalar-Gauss-Bonnet theory. The data used for training and validation is obtained by solving numerically the reduced field equations in the case of a static, spherically symmetric black holes. The neural network is trained using stochastic gradient descent, on top of which we add two mechanisms to aid convergence, namely a cyclical (sinusoidal) learning rate and a type of gradient normalization. We achieve a mean squared error over the whole dataset of roughly 8 × 10 −7 after 5000 epochs.