Persamaan Gelombang Satu Dimensi dengan Menggunakan Metode Neural Network

Fardika Armawanto, Wawan Kurniawan, Diana Endah Handayani

Abstract


Abstrak. Persamaan gelombang yang berupa persamaan differesial parsial akan diselesaikan secara numerik menggunakan finite diference explicit dan Neural Network. Hasil dari penyelesaian secara numerik menggunakan finite diference explicit akan dilakukan uji stabilitas. Setelah didapatkan kondisi yang stabil maka hal tersebut dinyatakan valid. Sehinhgga, dari hasil finite diference explicit yang valid dapat di bandingkan dengan metode Neural Network. Sementara itu, keberhasilan Neural Network sangat tergantung pada besarnya epochs yang terjadi pada pemograman dan hasil tersebut dapat dievaluasi dari hasil train loss dan  test loss.

Kata kunci: persamaan gelombang, finite diference, Neural Network

Abstract. The wave equation in the form of partial differential equation will be solved numerically using finite diference explicit and Neural Network. The results of the numerical solution using finite diference explicit will be tested for stability. After obtaining a stable condition, it is declared valid. Thus, the valid results of explicit finite diference can be compared with the Neural Network method. Meanwhile, the success of the Neural Network is highly dependent on the number of epochss that occur in the programming and these results can be evaluated from the results of train loss and test loss.

Keywords: wave equation, finite diference, Neural Network

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References


H. J. (Herbert J. Pain, The physics of vibrations and waves. John Wiley, 2005.

S. Alkhadhr and M. Almekkawy, “Wave Equation Modeling via Physics-Informed Neural Networks: Models of Soft and Hard Constraints for Initial and Boundary Conditions,” Sensors, vol. 23, no. 5, Mar. 2023, doi: 10.3390/s23052792.

A. N. Chasamah, M. Jamhuri, and E. Alisah, “Solusi Numerik Persamaan Gelombang Dua Dimensi Dengan Metode Beda Hingga Skema Eksplisit CTCS,” Jurnal Riset Mahasiswa Matematika, vol. 1, no. 1, pp. 14–22, Oct. 2021, doi: 10.18860/jrmm.v1i1.13411.

K. Mahmoodi, H. Ghassemi, and A. Heydarian, “Solving the Nonlinear Two-Dimension Wave Equation Using Dual Reciprocity Boundary Element Method,” International Journal of Partial Differential Equations and Applications, vol. 5, no. 1, pp. 19–25, Aug. 2017, doi: 10.12691/ijpdea-5-1-3.

F. Mirzaee and S. Bimesl, “A new approach to numerical solution of second-order linear hyperbolic partial differential equations arising from physics and engineering,” Results Phys, vol. 3, pp. 241–247, Nov. 2013, doi: 10.1016/j.rinp.2013.10.002.

W. W. Hsieh and B. Tang, “Applying Neural Network Models to Prediction and Data Analysis in Meteorology and Oceanography,” 1998.

M. C. Deo and C. Sridhar Naidu, “Real time wave forecasting using Neural Networks,” 1999.

T. W. Hughes, I. A. D. Williamson, M. Minkov, and S. Fan, “A P P L I E D P H Y S I C S Wave physics as an analog recurrent Neural Network,” 2019. [Online]. Available: https://www.science.org

L. R. Lines, R. Slawinski, and R. Phillip Bording, “Short Note A recipe for stability of finite-difference wave-equation computations.” [Online]. Available: http://library.seg.org/

A. Hosni Elhewy, E. Mesbahi, and Y. Pu, “Reliability analysis of structures using Neural Network method,” Probabilistic Engineering Mechanics, vol. 21, no. 1, pp. 44–53, Jan. 2006, doi: 10.1016/j.probengmech.2005.07.002.

“takayama1999”.

F. Chen et al., “NeuroDiffEq: A Python package for solving differential equations with Neural Networks,” J Open Source Softw, vol. 5, no. 46, p. 1931, Feb. 2020, doi: 10.21105/joss.01931.

S. Akthar, “A Study on Neural Network Architectures,” 2016. [Online]. Available: www.iiste.org

A. Bihlo and R. O. Popovych, “Physics-informed Neural Networks for the shallow-water equations on the sphere,” Apr. 2021, doi: 10.1016/j.jcp.2022.111024.

S. Cedillo, A. G. Núñez, E. Sánchez-Cordero, L. Timbe, E. Samaniego, and A. Alvarado, “Physics-Informed Neural Network water surface predictability for 1D steady-state open channel cases with different flow types and complex bed profile shapes,” Adv Model Simul Eng Sci, vol. 9, no. 1, Dec. 2022, doi: 10.1186/s40323-022-00226-8.

A. Alguacil, M. Bauerheim, M. C. Jacob, and S. Moreau, “Predicting the propagation of acoustic waves using deep convolutional Neural Networks,” J Sound Vib, vol. 512, Nov. 2021, doi: 10.1016/j.jsv.2021.116285.

C. Anitescu, E. Atroshchenko, N. Alajlan, and T. Rabczuk, “Artificial Neural Network methods for the solution of second order boundary value problems,” Computers, Materials and Continua, vol. 59, no. 1, pp. 345–359, 2019, doi: 10.32604/cmc.2019.06641.

A. Siahkoohi, M. Louboutin, and F. J. Herrmann, “Neural Network augmented wave-equation simulation,” Sep. 2019, [Online]. Available: http://arxiv.org/abs/1910.00925

T. de Wolff, H. Carrillo, L. Martí, and N. Sanchez-Pi, “Towards Optimally Weighted Physics-Informed Neural Networks in Ocean Modelling,” Jun. 2021, [Online]. Available: http://arxiv.org/abs/2106.08747

W. E. Sorteberg, S. Garasto, A. S. Pouplin, C. D. Cantwell, and A. A. Bharath, “Approximating the solution to wave propagation using deep Neural Networks,” Dec. 2018, [Online]. Available: http://arxiv.org/abs/1812.01609

D. A. Pratama, M. A. Bakar, N. B. Ismail, and M. Mashuri, “ANN-based methods for solving partial differential equations: a survey,” Arab Journal of Basic and Applied Sciences, vol. 29, no. 1. Taylor and Francis Ltd., pp. 233–248, 2022. doi: 10.1080/25765299.2022.2104224.




DOI: https://doi.org/10.26877/lpt.v3i1.18011

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