Pengembangan dan evaluasi kinerja model physics-informed neural network untuk pemecahan masalah maju dan invers pada persamaan diferensial parsial = Development and performance evaluation of physics-informed neural network in solving forward and inverse problems of partial differential equations

Chandrasukmana, Yohan (2023) Pengembangan dan evaluasi kinerja model physics-informed neural network untuk pemecahan masalah maju dan invers pada persamaan diferensial parsial = Development and performance evaluation of physics-informed neural network in solving forward and inverse problems of partial differential equations. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Dengan berkembangnya sains dan teknologi, pemecahan masalah terkait persamaan diferensial parsial (PDP) menjadi semakin dibutuhkan. Pada tugas akhir ini, diimplementasi model physics-informed neural network (PINN), sebuah pemecah PDP dan pencari parameter PDP berbasis kecerdasan komputasional. Proses training model PINN dilakukan dengan optimizer L-BFGS, SGD, dan Adam. Kemudian, dikembangkan model Hybrid PINN (H-PINN), sebuah modifikasi dari model PINN untuk pencarian parameter PDP yang mengutamakan fitting model dengan data di tahap awal learning. Diperkenalkan juga sebuah learning rate scheduler untuk optimizer berbasis gradien yang menggabungkan scheduler exponential dan piecewise constant decay. Efektivitas model PINN dan H-PINN diperlihatkan pada implementasinya terhadap masalah maju dan invers terkait persamaan panas dan persamaan KdV sebanyak lima kali percobaan. Kinerja dari model dievaluasi dengan galat relatif Frobenius norm dan analisis sifat fisika pada prediksi model. Pada kasus masalah maju, diperoleh solusi perubahan suhu panas dan pergerakan gelombang soliter KdV yang sesuai dengan sifat fisika yang ada dengan keakuratan yang tinggi. Pada kasus masalah invers, model PINN berhasil dilatih untuk memperoleh parameter PDP yang konvergen ke parameter yang sebenarnya. Kinerja model terbaik diperoleh dengan penggunaan optimizer Adam dengan learning rate kombinasi yang diajukan. Model H-PINN juga memiliki kinerja yang unggul ketika diberikan tebakan awal parameter PDP yang jauh dari nilai yang sebenarnya./With the development of science and technology, solutions to partial differential equations (PDEs) problems are becoming essential. In this thesis, a physics-informed neural network (PINN), which is an artificial intelligence-based PDE solver and parameter estimator, is implemented and trained with three optimizers: L-BFGS, SGD, and Adam. A novel modification of PINN for the parameter identification setting, hybrid PINN (H-PINN), is introduced. H-PINN prioritizes model fitting with data before minimizing the given PDE structure to find its parameters. A novel learning rate scheduler for gradient-based optimizers is also proposed. It combines exponential decay and piecewise constant decay learning rate schedulers. The effectiveness of PINN and H-PINN is demonstrated by solving the forward and inverse problems of the heat equation and Korteweg-De Vries equation. The model trial is done five times with L-BFGS, SGD, and Adam. The model’s performance is evaluated using the Frobenius norm in calculating relative error and analyzing any physical properties captured in the predicted solution. For the forward problems, model implementation results in a change in the given heat’s temperature and movement of solitary wave solutions which are consistent with their actual physical properties and predicted with high accuracy. For the inverse problems, PINN has successfully been trained to predict PDE parameters accurately. The best model performance is obtained by training with Adam and the proposed combined learning rate. H-PINN was also found to be superior when given an initial PDE parameter far from its actual value.

Item Type: Thesis (Bachelor)
Creators:
CreatorsNIMEmail
Chandrasukmana, YohanNIM01112190011chandrasukmanayohan@gmail.com
Contributors:
ContributionContributorsNIDN/NIDKEmail
Thesis advisorMargaretha, HelenaNIDN0312057504helena.margaretha@uph.edu
Thesis advisorSaputra, Kie Van IvankyNIDN0401038203kie.saputra@uph.edu
Uncontrolled Keywords: komputasi ilmiah; kecerdasan komputasional; persamaan diferensial parsial; physics-informed neural network; optimizer; gelombang soliton; kinerja model; scientific computing; artificial intelligence; partial differential equations; solitons; 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: Yohan Chandrasukmana
Date Deposited: 26 Jan 2023 01:20
Last Modified: 26 Jan 2023 01:20
URI: http://repository.uph.edu/id/eprint/52850

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