Infinite Order Systems of Differential Equations and Large Scale Random Neural Networks

2017 ◽  
pp. 183-195
Author(s):  
Soltan K. Kanzitdinov ◽  
Sergey A. Vasilyev
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Large Scale ◽  
Infinite Order ◽  
Systems Of Differential Equations ◽  
Random Neural Networks

scholarly journals USING OF MULTILAYER NEURAL NETWORKS FOR THE SOLVING SYSTEMS OF DIFFERENTIAL EQUATIONS

2021 ◽  
pp. 81-88
Author(s):  
Natalia Marchenko ◽  
Ganna Sydorenko ◽  
Roman Rudenko
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Loss Function ◽  
Initial Conditions ◽  
Solution Process ◽  
Analytical Form ◽  
Individual Values ◽  
Systems Of Differential Equations ◽  
Solving Equations ◽  
Multilayer Neural Networks

The article considers the study of methods for numerical solution of systems of differential equations using neural networks. To achieve this goal, thefollowing interdependent tasks were solved: an overview of industries that need to solve systems of differential equations, as well as implemented amethod of solving systems of differential equations using neural networks. It is shown that different types of systems of differential equations can besolved by a single method, which requires only the problem of loss function for optimization, which is directly created from differential equations anddoes not require solving equations for the highest derivative. The solution of differential equations’ system using a multilayer neural networks is thefunctions given in analytical form, which can be differentiated or integrated analytically. In the course of this work, an improved form of constructionof a test solution of systems of differential equations was found, which satisfies the initial conditions for construction, but has less impact on thesolution error at a distance from the initial conditions compared to the form of such solution. The way has also been found to modify the calculation ofthe loss function for cases when the solution process stops at the local minimum, which will be caused by the high dependence of the subsequentvalues of the functions on the accuracy of finding the previous values. Among the results, it can be noted that the solution of differential equations’system using artificial neural networks may be more accurate than classical numerical methods for solving differential equations, but usually takesmuch longer to achieve similar results on small problems. The main advantage of using neural networks to solve differential equations` system is thatthe solution is in analytical form and can be found not only for individual values of parameters of equations, but also for all values of parameters in alimited range of values.

scholarly journals Outdoor Node Localization Using Random Neural Networks for Large-Scale Urban IoT LoRa Networks

Algorithms ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 307
Author(s):  
Winfred Ingabire ◽  
Hadi Larijani ◽  
Ryan M. Gibson ◽  
Ayyaz-UI-Haq Qureshi
Keyword(s):  
Neural Networks ◽  
Long Range ◽  
Urban Areas ◽  
Large Scale ◽  
Low Cost ◽  
Wireless Sensor ◽  
Node Localization ◽  
Positioning Systems ◽  
Power Characteristics ◽  
Random Neural Networks

Accurate localization for wireless sensor end devices is critical, particularly for Internet of Things (IoT) location-based applications such as remote healthcare, where there is a need for quick response to emergency or maintenance services. Global Positioning Systems (GPS) are widely known for outdoor localization services; however, high-power consumption and hardware cost become a significant hindrance to dense wireless sensor networks in large-scale urban areas. Therefore, wireless technologies such as Long-Range Wide-Area Networks (LoRaWAN) are being investigated in different location-aware IoT applications due to having more advantages with low-cost, long-range, and low-power characteristics. Furthermore, various localization methods, including fingerprint localization techniques, are present in the literature but with different limitations. This study uses LoRaWAN Received Signal Strength Indicator (RSSI) values to predict the unknown X and Y position coordinates on a publicly available LoRaWAN dataset for Antwerp in Belgium using Random Neural Networks (RNN). The proposed localization system achieves an improved high-level accuracy for outdoor dense urban areas and outperforms the present conventional LoRa-based localization systems in other work, with a minimum mean localization error of 0.29 m.

SOLUTION OF SOME SYSTEMS OF DIFFERENTIAL EQUATIONS IN MATHEMATICAL SYSTEM MAPLE

2013 ◽  
Vol 1 (05) ◽  
pp. 58-65
Author(s):  
Yunona Rinatovna Krakhmaleva ◽  
◽  
Gulzhan Kadyrkhanovna Dzhanabayeva ◽  
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations ◽  
Mathematical System

A Developmental Method for Evolving Large-Scale Spiking Neural Networks

2012 ◽  
Vol 35 (12) ◽  
pp. 2633 ◽  
Author(s):  
Xiang-Hong LIN ◽  
Tian-Wen ZHANG ◽  
Gui-Cang ZHANG
Keyword(s):  
Neural Networks ◽  
Large Scale ◽  
Spiking Neural Networks
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