Deep neural network method for solving the fractional Burgers-type equations with conformable derivative

作者：Yinlin Ye, Xinyi Liu, Yajing Li, Hongtao Fan, Hongbing Zhang · 发表于：Physica Scripta · 年份：2023 · DOI：10.1088/1402-4896/acd307 · 被引用次数：16 · 研究领域：Fractional Differential Equations Solutions、Model Reduction and Neural Networks、Numerical methods in engineering

Abstract In this article, we introduce the modified physics-informed neural network (PINN) method for finding data-driven solutions of three classes of time-fractional Burgers-type equations under the conformable sense. Since conformable derivative satisfies the chain rule, automatic differentiation can be applied to compute it directly to avoid truncation and other numerical discretization. In addition, the locally adaptive activation function and two effective weighting strategies are introduced to improve solution accuracy. As a result, three numerical examples indicate that the modified PINN method gives an efficient and reliable solution.