شماره ركورد كنفرانس :
5263
عنوان مقاله :
A high-order fractional physics-informed neural network (fPINN) for solving time fractional diffusion equations with Caputo derivatives
پديدآورندگان :
Mostajeran Farinaz f_mostajeran@modares.ac.ir Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, 14115-175, Iran. , Hosseini Seyed Mohammad hossei_m@modares.ac.ir Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, 14115-175, Iran.
كليدواژه :
Caputo derivative , fPINN , a high , order numerical method , time fractional diffusion equations
عنوان كنفرانس :
54 امين كنفرانس رياضي ايران
چكيده فارسي :
In this paper, a high-order fractional physics-informed neural network (fPINN) for solving time fractional diffusion equations with Caputo derivatives is presented. To design the scheme, the Caputo temporal derivative is approximated using a high-order method, named L1-2-3. Then we use the physics-informed neural network (PINN) to employ automatic differentiation and minimize the cost function with respect to the neural network parameters. We prove that the loss function converges to zero and illustrate the effectiveness of the method by providing numerical examples.
