E-PINN：针对高阶非线性积分微分方程正演和反演问题的扩展物理信息神经网络

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

International Journal of Computer Mathematics Pub Date : 2024-07-09 DOI:10.1080/00207160.2024.2374820

HongMing Zhang, Xinping Shao, ZhengFang Zhang, MingYan He

引用次数: 0

摘要

物理信息神经网络（PINN）是一种新的深度学习范式，它在损失函数中嵌入了由PDE划定的物理信息，并优化了神经网络中的权重...

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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E-PINN: extended physics informed neural network for the forward and inverse problems of high-order nonlinear integro-differential equations

Physics informed neural network (PINN) is a new deep learning paradigm, which embeds the physical information delineated by PDEs in the loss function and optimizes the weights in the neural network...

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来源期刊

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

期刊介绍： International Journal of Computer Mathematics (IJCM) is a world-leading journal serving the community of researchers in numerical analysis and scientific computing from academia to industry. IJCM publishes original research papers of high scientific value in fields of computational mathematics with profound applications to science and engineering. IJCM welcomes papers on the analysis and applications of innovative computational strategies as well as those with rigorous explorations of cutting-edge techniques and concerns in computational mathematics. Topics IJCM considers include: • Numerical solutions of systems of partial differential equations • Numerical solution of systems or of multi-dimensional partial differential equations • Theory and computations of nonlocal modelling and fractional partial differential equations • Novel multi-scale modelling and computational strategies • Parallel computations • Numerical optimization and controls • Imaging algorithms and vision configurations • Computational stochastic processes and inverse problems • Stochastic partial differential equations, Monte Carlo simulations and uncertainty quantification • Computational finance and applications • Highly vibrant and robust algorithms, and applications in modern industries, including but not limited to multi-physics, economics and biomedicine. Papers discussing only variations or combinations of existing methods without significant new computational properties or analysis are not of interest to IJCM. Please note that research in the development of computer systems and theory of computing are not suitable for submission to IJCM. Please instead consider International Journal of Computer Mathematics: Computer Systems Theory (IJCM: CST) for your manuscript. Please note that any papers submitted relating to these fields will be transferred to IJCM:CST. Please ensure you submit your paper to the correct journal to save time reviewing and processing your work. Papers developed from Conference Proceedings Please note that papers developed from conference proceedings or previously published work must contain at least 40% new material and significantly extend or improve upon earlier research in order to be considered for IJCM.