Sim, Fabio Milentiansen and Budiarto, Eka and Rusyadi, Rusman (2020) Neural Solvers for Differential Equations Applied in Physical Systems. Bachelor thesis, Swiss German University.

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Abstract

Differential equations are ubiquitous in many fields of study, yet analytical solutions to such equations, whether ordinary or partial, have long eluded discovery. With the advent of modern deep learning, neural networks have become a viable alternative to numerical methods. By reformulating the problem as an optimisation task, neural networks can be trained to approximate nonlinear solutions. In this paper, neural solvers are implemented in TensorFlow for a variety of equations. Their overall performance is analysed and even found to surpass traditional schemes in certain cases. Experimental data is also used to validate the neural solutions. Stiff and nonlinear systems of equations are attempted as well, and the stability of the method is investigated. A normalisation technique, akin to feature scaling for supervised learning, is proposed and shown to achieve superior convergence. Although neural solvers will not replace the computational speed offered by traditional schemes in the near future, they remain a feasible, easy-to-implement substitute when all else fails.

Item Type:	Thesis (Bachelor)
Uncontrolled Keywords:	Differential Equations; Deep Learning; Neural Networks; Numerical Analysis; Computer Simulation
Subjects:	Q Science > QA Mathematics > QA76 Computer software Q Science > QA Mathematics > QA76 Computer software > QA76.87 Neural networks (Computer science) T Technology > TJ Mechanical engineering and machinery T Technology > TJ Mechanical engineering and machinery > TJ163.12 Mechatronics
Divisions:	Faculty of Engineering and Information Technology > Department of Mechatronics Engineering
Depositing User:	Faisal Ifzaldi
Date Deposited:	02 Nov 2020 14:10
Last Modified:	02 Nov 2020 14:10
URI:	http://repository.sgu.ac.id/id/eprint/1952

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