PENDEKATAN DEEP LEARNING UNTUK MEMPREDIKSI ENERGI KEADAAN DASAR BERDASARKAN POTENSIAL OSILATOR HARMONIK SEDERHANA DUA DIMENSI

Achmad Jaelani; Teguh Budi Prayitno; Yanoar Pribadi Sarwono

doi:10.21009/03.1201.FA38

Achmad Jaelani Program Studi Fisika, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Negeri Jakarta, Jakarta Timur 13220, Indonesia
Teguh Budi Prayitno Program Studi Fisika, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Negeri Jakarta, Jakarta Timur 13220, Indonesia
Yanoar Pribadi Sarwono Pusat Riset Fisika Kuantum, Badan Nasional dan Inovasi Nasional, Tangerang Selatan 15314, Indonesia

DOI: https://doi.org/10.21009/03.1201.FA38

Abstract

Abstrak

Penelitian ini mengusulkan pendekatan deep learning untuk memprediksi energi keadaan dasar elektron berdasarkan potensial osilator harmonik sederhana dua dimensi dari persamaan Schrödinger. Metode ini menggunakan jaringan saraf konvolusi untuk mempelajari hubungan antara potensial dan energi keadaan dasar. Dataset osilator harmonik sederhana dihasilkan dengan fungsi skalar dimana parameter-parameter dihasilkan secara acak. Kinerja pendekatan yang diusulkan dibandingkan dengan metode numerik, seperti metode beda hingga. Hasil yang diperoleh menunjukkan bahwa pendekatan deep learning lebih efisien dan akurat dalam memprediksi energi keadaan dasar berdasarkan potensial osilator harmonik sederhana dua dimensi. Model mendapatkan mean squared error sebesar 6.37×10^-7 mHa pada data uji. Pendekatan ini memiliki potensi aplikasi dalam berbagai bidang, seperti ilmu material, komputasi kimia, dan mekanika kuantum.

Kata-kata kunci: Deep Learning, Persamaan Schrödinger, Energi Keadaan Dasar.

Abstract

This research proposes a deep learning approach to predict the ground state energy of an electron based on the two-dimensional simple harmonic oscillator potential of the Schrödinger equation. The approach uses convolutional neural networks to learn the relationship between the potential and the ground state energy. The simple harmonic oscillator dataset is generated with a scalar function where the parameters are randomly generated. The performance of the proposed approach is compared with numerical methods, such as the finite difference methods. The results show that the deep learning approach is more efficient and accurate in predicting the ground state energy based on the two-dimensional simple harmonic oscillator potential, achieving a mean squared error of 6.37×10^-7 mHa on the test data. This remarkable performance demonstrates the potential of the proposed approach for applications in various fields, including material science and quantum mechanics.

Keywords: Deep Learning, Schrödinger Equation, Ground State Energy.

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