Research on differential solution based on aligned transformer

With the rapid development of deep learning, artificial intelligence has achieved great success in the field of natural language processing and has shown strong ability to deal with complex problems. Applying neural machine translation technology in this field to symbolic computing problems can not only overcome the limitations of computational algebra systems in solving complex symbolic computing problems, but also expand the application scope of artificial intelligence in symbolic computing. Therefore, this paper applies neural machine translation to symbolic computing tasks. At present the research on differential equations in deep learning mainly focuses on numerical solutions and lacks research on analytical solutions. At the same time in order to expand the application of neural networks in symbolic computing this paper proposes a method of constructing partial differential equation data sets and introduces alignment to solve differential equations. The dataset is generated inversely by the equation solution mapping to the equation: Combining the transformation of ordinary differential equations with characteristic line method, the first-order linear with constant coefficients, the first-order linear with variable coefficients and the second-order parabolic partial differential equations satisfying certain conditions are generated. In addition, word alignment is introduced into Transformer for multi-task learning of translation and alignment to improve the model solving effect. The experimental results show that the model improves 2.09, 0.58 and 0.96 percentage points in solving first-order linear constant coefficients, first-order linear variable coefficients and second-order parabolic partial differential equations satisfying a certain condition compared with the conventional Transformer model, and its performance is better than that of SymPy and Mathematica.