Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation

no code implementations • 14 Sep 2023 • Yuesheng Xu, Taishan Zeng

We develop in this paper a multi-grade deep learning method for solving nonlinear partial differential equations (PDEs).

Sparse Deep Neural Network for Nonlinear Partial Differential Equations

no code implementations • 27 Jul 2022 • Yuesheng Xu, Taishan Zeng

Noting that DNNs have an intrinsic multi-scale structure which is favorable for adaptive representation of functions, by employing a penalty with multiple parameters, we develop DNNs with a multi-scale sparse regularization (SDNN) for effectively representing functions having certain singularities.