福州大学学报（自然科学版）2024，Vol.52Issue(4)：379-386,8.DOI:10.7631/issn.1000-2243.23067
基于深度学习的分数阶Nernst-Plank方程求解
Solution of fractional Nernst-Plank equation based on deep learning
摘要
Abstract
This paper used fractional physics-informed neural networks(fPINN)to solve the time-fractional equation,and demonstrate its accuracy and effectiveness in solving the forward and inverse problems of time-fractional N-P.Moreover,the paper explain result by analyzing the three sources of numerical errors due to discretization,sampling and optimization.The paper also analyze relative between the discretization and sampling error.The paper find that there exists the best training point set size to minimize the solution error with fixed discretization error.Finally,the paper demonstrate the effectiveness of NN in solving inverse problems.关键词
分数阶物理信息神经网络/深度学习/时间分数阶Nernst-Plank方程/误差分析Key words
fractional physics-informed neural networks(fPINN)/deep learning/time-fractional Nernst-Plank/numerical error analysis分类
数理科学引用本文复制引用
徐国泰,李娴娟,宋方应..基于深度学习的分数阶Nernst-Plank方程求解[J].福州大学学报（自然科学版）,2024,52(4):379-386,8.基金项目
国家自然科学基金资助项目(12022102) （12022102）
福建省自然科学基金资助项目(2023J01263) （2023J01263）
