Systematic Construction of Neural Forms for Solving Partial Differential Equations Inside Rectangular Domains, Subject to Initial, Boundary and Interface Conditions

被引：44

作者：

Lagari, Pola Lydia ^{[1
]}

Tsoukalas, Lefteri H. ^{[1
]}

Safarkhani, Salar ^{[2
]}

Lagaris, Isaac E. ^{[3
]}

机构：

[1] Purdue Univ, Sch Nucl Engn, W Lafayette, IN 47907 USA

[2] Purdue Univ, Sch Mech Engn, W Lafayette, IN 47907 USA

[3] Univ Ioannina, Dept Comp Sci & Engn, Ioannina 45500, Greece

来源：

INTERNATIONAL JOURNAL ON ARTIFICIAL INTELLIGENCE TOOLS | 2020年 / 29卷 / 05期

关键词：

Interface conditions; neural forms; neural networks; partial differential equations; NETWORK METHODS;

D O I：

10.1142/S0218213020500098

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

A systematic approach is developed for constructing proper trial solutions to Partial Differential Equations (PDEs) of up to second order, using neural forms that satisfy prescribed initial, boundary and interface conditions. The spatial domain considered is of the rectangular hyper-box type. On each face either Dirichlet or Neumann conditions may apply. Robin conditions may be accommodated as well. Interface conditions that induce discontinuities, have not been treated to date in the relevant neural network literature. As an illustration a common problem of heat conduction through a system of two rods in thermal contact is considered.

引用

页数：12

共 42 条

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