Thermodynamics and Feature Extraction by Machine Learning

Abstract

Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the Renormalization Group (RG) flow of the lattice model. Our results suggest an alternative explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated to the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.

Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions

“…321) The deep neural network used here is a tool for classifying the phase and is regarded as a blackbox. The properties of the neural network themselves are also interesting to study from the physics view point , 187, especially in relation to the renormalization group [354][355][356][357][358][359][360][361][362] and tensor network. [363][364][365][366][367][368][369][370][371][372] The vulnerability of phase determination against adversarial perturbation is also an interesting topic.…”

Neural Monte Carlo Renormalization Group

“…Multiple layers of representation are used to learn distinct features directly from the training data. The similarity between the structure of the DNN and the course-graining schemes in statistical physics inspires many efforts to establish connection between variational RG [21] and unsupervised learning of DNN [22][23][24][25][26][27][28][29][30]. Here, we want to address a different question: how can we train an DNN to obtain an optimal RSRG transformation?…”

A high-bias, low-variance introduction to Machine Learning for physicists

“…In parallel, tools from Statistical Physics have been applied to analyze the learning ability of RBMs (Decelle et al, 2018;Huang, 2017b), characterizing the sparsity of the weights, the effective temperature, the non- linearities in the activation functions of hidden units, and the adaptation of fields maintaining the activity in the visible layer (Tubiana and Monasson, 2017). Spin glass theory motivated a deterministic framework for the training, evaluation, and use of RBMs (Tramel et al, 2017); it was demonstrated that the training process in RBMs itself exhibits phase transitions (Barra et al, 2016(Barra et al, , 2017; learning in RBMs was studied in the context of equilibrium (Cossu et al, 2018;Funai and Giataganas, 2018) and nonequilibrium (Salazar, 2017) thermodynamics, and spectral dynamics (Decelle et al, 2017); mean-field theory found application in analyzing DBMs (Huang, 2017a). Another interesting direction of research is the use of generative models to improve Monte Carlo algorithms (Cristoforetti et al, 2017;Nagai et al, 2017;Tanaka and Tomiya, 2017b;Wang, 2017).…”