Application Of Machine Learning In Thermodynamic Phase And Quantum Dynamics

Machine learning has excellent capabilities of classification,recognition,fitting and interpretability that has a wide range of applications in the field of physics.The application of machine learning in physics is special compared to conventional numerical methods.Machine learning can find a new way of explaining physical quantities without human prior knowledge,and even discover new physical properties.In fact,in identifying phase transitions in physics,whether thermodynamic phase or topological phase,machine learning has done a lot of work without any awareness of the concept of phase.Many phenomena in physics correspond to results,but some special methods are usually required to explain clearly between phenomena and results.Machine learning acts as a composite function connecting input and output,and can also act as an interpreter.Physical phenomena are fed into machine learning algorithms as inputs,and then the corresponding outputs are used to simulate the results.Interpretable machine learning can serve as a bridge between phenomena and observations,explaining the relationship between them.There are four chapters in this thesis.In Chapter 1,we briefly introduced the fundamental concepts in machine learning,including neural networks,decision trees,loss functions,and optimizers.We give a brief introduction to two concepts in interpretable machine learning,namely global interpretability and local interpretability.We also introduce quantum dynamics of open systems,illustrating and generalizing Markov processes,system environment evolution,and GKSL master equations.In Chapter 2,we conduct a study on the thermodynamic phase of tree-based interpretable machine learning.The basic concept in the boosting tree algorithm is boosting.The basic idea of boosting is to combine many weak learners into a strong learner.After multiple boosting iterations,the predictions of a series of weak classifiers are combined into a final prediction through weighted majority voting.We use an improved version of the boosting tree,xgboost algorithm,to simulate thermodynamic phase transitions in a two-dimensional square lattice model with five interactions with high accuracy.The global feature importance in the xgboost algorithm can be measured by weight,total gain and gain.With these three metrics,we can derive a ranking of the importance of temperature and the five interactions on the phase transition.The tree SHAP algorithm can be used to measure the contribution of the input features to the phase transition,and the importance ranking by tree SHAP is consistent with the ranking in the xgboost algorithm.The tree SHAP algorithm can also measure the direction of influence of the input features on the phase transition.In Chapter 3,we study dynamical learning of non-Markovian quantum dynamics.An open quantum system is a quantum system with a coupled environment of the system,and its dynamics can be found by solving the equations of motion of the reduced state.The density operator of the system cannot be obtained from a single measurement,so any information about the system can only be obtained from a series of measurements.On the other hand,since each measurement will inevitably cause interference to the measurement object,the measurement itself will cause some difficulties in the analysis of the system evolution.Non-Markovian quantum dynamics means that the dynamical evolution does not only depend on the current system state and evolution rules,but also needs to consider the dynamical behavior at all past evolutionary times.We first consider using supervised learning to directly simulate the Hamiltonian of quantum systems,and get the results for analysis.In fact,directly simulating the Hamiltonian of an open system and then restoring the non-Markovian quantum dynamics has certain limitations.When the loss function,that is,the log-likelihood,is optimized to a predetermined value,there is still a non-negligible error between the Hamiltonian simulated by supervised learning and the actual Hamiltonian,which causes the simulated dynamics to fail to fit the actual dynamics.We use dynamical learning to simulate non-Markovian quantum dynamics.Dynamical learning is divided into two stages,the first stage is the pre-training of the weights,and the second stage is the neural network with fixed weights.Instead of simulating the Hamiltonian,dynamic learning directly simulates the density operator of non-Markovian quantum dynamics.A neural network with static weights in dynamical learning can better give dynamic properties.In Chapter 4,we summarize the entire paper and provide an overview of interpretable machine learning and dynamical learning.