Determining degrees of freedom with deep learning algorithms

U ovom radu predstavljena je metodologija za određivanje kritične temperature fizikalnih sustava. Metoda se zasniva na korištenju neuronskih mreža čija se arhitektura ponaša poput renormalizacijske grupe (RG). Metodologija je primijenjena na 2D Isingovom modelu za tri različite rešetke: kvadratnu, trokutastu i heksagonalnu. Naučena su tri generativna modela koji imaju ulogu RG-a, a to su: ograničen Boltzmannov stroj, varijacijski autoenkoder i generativne suparničke mreže. Iterativnom primjenom generativnih modela generiramo sustave u blizini kritične temperature. Temperature sustava određene su pomoću naučene neuronske mreže. Također je primijenjena i metoda bez generatora koja se zasniva na iterativnoj primjeni normalizacije skrivenih vektora mreže. Metoda bez generatora i ograničen Boltzmannov stroj daju dobre i stabilne rezultate za sve tri rešetke, dok varijacijskom autoenkoderu i generativnim suparničkim mrežama točnost varira od rešetke do rešetke.This thesis presents a methodology for determining the critical temperature of a physical system. The method is based on neural networks that behave like a renormalization group (RG). The methodology was applied to the 2D Ising model on three different lattices: square, triangular, and hexagonal. Three generative models that behave like the RG have been trained, namely: a restricted Boltzmann machine, a variational autoencoder, and generative adversarial networks. By iteratively applying generative models to the data, we obtained systems close to the critical temperature. System temperatures were measured using a neural network that was trained for this purpose. A generator free method based on the iterative application of normalization on the network’s hidden vectors is also applied. The generator-free method and the limited Boltzmann machine give good and stable results for all three lattices, while the variation of the autoencoder and generative adversarial networks vary from lattice to lattice