Deep neural network method for solving the fractional Burgers-type equations with conformable derivative
Yinlin Ye, Xinyi Liu, Yajing Li, Hongtao Fan, Hongbing Zhang
Abstract
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.
Topics & Concepts
Conformable matrixDiscretizationFractional calculusArtificial neural networkType (biology)Truncation (statistics)Applied mathematicsDerivative (finance)Computer scienceWeightingMathematicsMathematical analysisArtificial intelligencePhysicsBiologyQuantum mechanicsMachine learningAcousticsFinancial economicsEconomicsEcologyFractional Differential Equations SolutionsModel Reduction and Neural NetworksNumerical methods in engineering