Solving Symbol Regression Base On Deep Learning

We can collect a lot of data in production and life.In order to better understand the mathematical and physical significance behind these dataset,we can use symbol regression to fit these data.Symbol regression is a problem which searches for a formula to describe the dataset within the specified symbol space.Symbol regression is a NP problem,which is usually solved by Genetic Programming(GP).Owing to the disadvantage of random search and forgotten most intermedia results,GP often has a long time to search and is easy to fall into local optimum solutions.In order to overcome the above disadvantages,this paper introduces the method of Deep Learning into the problem of symbol regression.Deep Learning can discover hidden features in the data to guide the formula generation process.In order to solve the problem of no coefficient symbol regression,a symbol regression algorithm based on Convolution Neural Network(CNN-SR)is proposed.Firstly,the generate feature of the formula is studied using the Convolutional Neural Network,and then the target formula is restored using the neural network according to the given target dataset.It is proved by experiment that compared with GP algorithm,the CNN-SR algorithm can find the target formula quickly and effectively.In order to solve the problem of symbol regression with coefficients,we propose a symbol regression algorithm based on Monte Carlo Tree Search(MCTS-SR).The MCTS-SR algorithm divides the symbol space into model space and coefficient space.Then,under the guidance of deep policy network,the Monte Carlo Tree Search is used to look for a formula model for finding suitable dataset features in the model space.On this basis,the particle swarm algorithm is used to search the coefficient space under this formula model.Experimental results show that,compared with GP algorithm,the algorithm can have a lower fitness value,and is hard to fall into local optimum solutions.In order to reduce the artificial interference factors in the MCTS-SR algorithm,and the training dataset can be dynamically changed,we propose a symbol regression algorithm based on Reinforcement Learning(RL-SR).RL-SR algorithm uses DQN algorithm to train neural network.,compared with the traditional supervised training,RL-SR algorithm can train the formula generation process of a whole path at a time,and the training dataset is added in the training process.Experimental results show that this method can achieve dynamic training,and the fitness value is lower than GP method.