An improved data-free surrogate model for solving partial differential equations using deep neural networks

MLA

Jie Liu, et al. “An Improved Data-Free Surrogate Model for Solving Partial Differential Equations Using Deep Neural Networks.” Scientific Reports, vol. 11, Sept. 2021. EBSCOhost, https://doi.org/10.1038/s41598-021-99037-x.

APA

Jie Liu, Rongliang Chen, Qian Wan, Rui Xu, & Xinhai Chen. (2021). An improved data-free surrogate model for solving partial differential equations using deep neural networks. Scientific Reports, 11. https://doi.org/10.1038/s41598-021-99037-x

Chicago

Jie Liu, Rongliang Chen, Qian Wan, Rui Xu, and Xinhai Chen. 2021. “An Improved Data-Free Surrogate Model for Solving Partial Differential Equations Using Deep Neural Networks.” Scientific Reports 11 (September). doi:10.1038/s41598-021-99037-x.