Wicaksono, Fakhri Bimo (2025) Penerapan model physics-informed neural network untuk mencari solusi numerik pada persamaan diferensial biasa = Application of physics-informed neural network model to find numerical solutions of ordinary differential equations. Bachelor thesis, Universitas Pelita Harapan.
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Abstract
Seiring dengan perkembangan sains dan teknologi, semakin dibutuhkan pemodelan matematika yang dapat mengaproksimasi realitas berdasarkan hukum fisika. Physics-Informed Neural Network (PINN) merupakan metode deep learning yang menggabungkan prinsip fisika melalui persamaan diferensial ke dalam proses pelatihan jaringan saraf. Dalam penelitian ini, PINN digunakan untuk menyelesaikan Persamaan Diferensial Biasa (PDB), baik yang bersifat linier maupun non-linier. Pendekatan ini dilakukan dengan adanya solusi analitik dan menggunakan prediksi dari solusi numerik seperti metode Runge-Kutta, karena loss function dalam training dikonstruksi dari bentuk persamaan diferensial yang ingin diselesaikan. Model PINN dikembangkan dengan arsitektur jaringan saraf feedforward dan dilatih menggunakan kombinasi optimasi Adam. Untuk mengevaluasi performa model, hasil dari PINN dibandingkan dengan solusi numerik dari metode Runge-Kutta Orde 4 (RK4). Hasil eksperimen menunjukkan bahwa PINN mampu menghasilkan solusi yang sangat mendekati solusi aslinya, baik secara visual maupun secara kuantitatif, serta menunjukkan ketahanan terhadap kompleksitas non-linieritas sistem PDB, dengan catatan bahwa terdapat solusi analitik maupun prediksi solusi numerik yang mendekati solusi aslinya. Dengan demikian, penelitian ini mendemonstrasikan bahwa PINN dapat digunakan sebagai metode alternatif dalam menyelesaikan PDB jika terdapat solusi analitik maupun numerik./With the development of science and technology, there is a need for mathematical modeling that can approximate reality based on the laws of physics. Physics-Informed Neural Network (PINN) is a deep learning method that incorporates physics principles through differential equations into the neural network training process. In this research, PINN is used to solve ordinary differential equations (ODE), both linear and non-linear. This approach is done in the presence of analytical solutions and uses predictions from numerical solutions such as the Runge-Kutta method, because the loss function in the training is constructed from the form of the differential equation to be solved. The PINN model is developed with a feedforward neural network architecture and trained using an Adam optimization. To evaluate the performance of the model, the results of PINN are compared with the analytical and numerical solution of the Fourth Order Runge-Kutta method (RK4). Experimental results show that PINN is able to produce solutions that are very close to the original solution, both visually and quantitatively, and shows robustness to the complexity of the non-linearity of the ODE system, provided that both the analytical solution and the predicted numerical solution are close to the original solution. Thus, this study demonstrates that PINN can be used as an alternative method in solving ODE if both analytical and numerical solutions exist.
Item Type: | Thesis (Bachelor) |
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Creators: | Creators NIM Email ORCID Wicaksono, Fakhri Bimo NIM01112190021 fbimo_wicaksono@yahoo.co.id UNSPECIFIED |
Contributors: | Contribution Contributors NIDN/NIDK Email Thesis advisor Saputra, Kie Van Ivanky NIDN0401038203 kie.saputra@uph.edu Thesis advisor Widjaja, Petrus NIDN0314095901 petrus.widjaja@uph.edu |
Uncontrolled Keywords: | komputasi ilmiah; deep learning; persamaan diferensial biasa; physics-informed neural network; solusi numerik; optimizer; kinerja model; scientific computing; ordinary differential equations; numerical solution; model performance evaluation |
Subjects: | Q Science > QA Mathematics |
Divisions: | University Subject > Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics |
Depositing User: | Fakhri Bimo Wicaksono |
Date Deposited: | 23 Jul 2025 04:42 |
Last Modified: | 23 Jul 2025 04:42 |
URI: | http://repository.uph.edu/id/eprint/70014 |