APPROXIMATING SOLUTIONS OF GOVERNING EQUATIONS USING FOURIER TRANSFORM AND SUPPORT VECTOR MACHINE

Ahmad Izzuddin, - and Lala Septem Riza, - and Muhammad Nursalman, - (2025) APPROXIMATING SOLUTIONS OF GOVERNING EQUATIONS USING FOURIER TRANSFORM AND SUPPORT VECTOR MACHINE. S1 thesis, Universitas Pendidikan Indonesia.

Abstract

Numerical models of systems are a crucial part of science and engineering. The use of machine learning in this space for operator learning provides an alternative as data-driven surrogates. The Fourier Transform provides a key component for learning the relationship between a function and its derivatives. Building on Spectral Neural Operators (SNO), we propose a Support Vector Machine (SVM) based framework to learn the underlying governing equations of a system based on data. We study the viability and interpretability of the proposed framework on the derivative equation and the Burgers’ equation. The model is able to learn from mathematically correct random data and is able to partially generalize to an exact solution of the Burgers’ equation. The learned model is interpreted and verified to have learned the correct contributions of the input function coefficients to the output function coefficients. Our proposed model performs up to 33 times faster than the traditional lsoda method when solving the Burgers’equation Model numerik sebuah sistem merupakan bagian penting dari ilmu pengetahuan dan engineering. Penggunaan Machine Learning (ML)dalamruanginiuntukpembelajaran operator menyediakan alternatif sebagai data-driven surrogates. Fourier Transform menyediakan komponen kunci untuk mempelajari hubungan antara suatu fungsi dan turunannya. Berdasarkan Spectral Neural Operators (SNO), kami mengusulkan kerangka kerja berbasis Support Vector Machine (SVM) untuk mempelajari persamaan dasar yang mengatur suatu sistem berdasarkan data. Kami mempelajari kelayakan dan interpretabilitas kerangka kerja yang diusulkan pada persamaan turunan dan persamaan Burgers. Model ini mampu belajar dari data acak yang secara matematis benar dan sebagian mampu melakukan generalisasi ke solusi eksak dari persamaan Burgers. Model yang dipelajari diinterpretasikan dan diverifikasi untuk mempelajari kontribusi yang benar dari koefisien fungsi masukan terhadap koefisien fungsi keluaran. Model yang diajukan menyelesaikan solusi Burgers’ equation hingga 33 kali lebih cepat daripada metode numerik tradisional lsoda

	Text S_KOM_1908919_Title.pdf Download (1MB)
	Text S_KOM_1908919_Chapter1.pdf Download (1MB)
	Text S_KOM_1908919_Chapter2.pdf Restricted to Staf Perpustakaan Download (396kB)
	Text S_KOM_1908919_Chapter3.pdf Download (325kB)
	Text S_KOM_1908919_Chapter4.pdf Restricted to Staf Perpustakaan Download (49MB)
	Text S_KOM_1908919_Chapter5.pdf Download (123kB)
	Text S_KOM_1908919_Appendix.pdf Restricted to Staf Perpustakaan Download (1MB)

Item Type:	Thesis (S1)
Additional Information:	ID SINTA Dosen Pembimbing Lala Septem Riza: 5975668 Muhammad Nursalman:
Uncontrolled Keywords:	Operator Learning, PDE, LSSVM Operator Learning, PDE, LSSVM.
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions:	Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Ilmu Komputer
Depositing User:	Alsa Kurnia Muhammad Rizky
Date Deposited:	21 Nov 2025 01:14
Last Modified:	21 Nov 2025 01:14
URI:	http://repository.upi.edu/id/eprint/134503

Actions (login required)

View Item