Adaptive Learning Neural Network Method for Solving Time–Fractional Diffusion Equations
Babak Shiri, Hua Kong, Guo–Cheng Wu, Cheng Luo
Abstract
A neural network method for solving fractional diffusion equations is presented in this letter. An adaptive gradient descent method is proposed to minimize energy functions. Due to the memory effects of the fractional calculus, the gradient of energy function becomes much more complicated, and we suggest a simplified method. Numerical examples with one-layer and two-layer neurons show the effectiveness of the method.
Topics & Concepts
Artificial neural networkGradient descentFractional calculusEnergy (signal processing)Function (biology)Balanced flowComputer scienceApplied mathematicsDiffusionLayer (electronics)MathematicsActivation functionAlgorithmMathematical analysisArtificial intelligencePhysicsOrganic chemistryChemistryStatisticsEvolutionary biologyBiologyThermodynamicsFractional Differential Equations SolutionsModel Reduction and Neural NetworksNeural Networks and Applications