近期，李东方教授团队的文章《Kernel-based PINNs for time fractional differential equations and Volterra integral-differential equations》在国际期刊《Physica D-Nonlinear Phenomena》发表。

      摘要：In this paper, we propose a novel kernel-based physics informed neural networks (kPINNs) framework for solving time fractional differential equations and Volterra integral differential equations. The highlights mainly consist of two aspects. On one hand, automatic differentiation can be applied more directly and effectively by the present framework. In contrast, the previous neural network approaches for such problems typically depend on difference discretization of the integral operator. On the other hand, to overcome the difficulties from the stiffness, the weights are incorporated into the loss functions. This allows the kPINNs to handle the stiff systems effectively. And the kPINNs can reduce computational cost and improve accuracy for high-dimensional problems. Comparative studies with existing neural network solvers and extensive numerical experiments are also presented to demonstrate the effectiveness and efficiency of our method.

      论文链接：https://webofscience.clarivate.cn/wos/alldb/full-record/WOS:001712793800001