Exploring the power of physics-informed neural networks for accurate and efficient solutions to 1D shallow water equations

Van Gian Nguyen; Van Linh Nguyen; Sungho Jung; Hyunuk An; Giha Lee

doi:10.3741/JKWRA.2023.56.12.939

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2023 Vol.56, Issue 12 Preview Page Next Page

Research Article

Exploring the power of physics-informed neural networks for accurate and efficient solutions to 1D shallow water equations 물리 정보 신경망을 이용한 1차원 천수방정식의 해석

31 December 2023. pp. 939-953

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Abstract

Shallow water equations (SWE) serve as fundamental equations governing the movement of the water. Traditional numerical approaches for solving these equations generally face various challenges, such as sensitivity to mesh generation, and numerical oscillation, or become more computationally unstable around shock and discontinuities regions. In this study, we present a novel approach that leverages the power of physics-informed neural networks (PINNs) to approximate the solution of the SWE. PINNs integrate physical law directly into the neural network architecture, enabling the accurate approximation of solutions to the SWE. We provide a comprehensive methodology for formulating the SWE within the PINNs framework, encompassing network architecture, training strategy, and data generation techniques. Through the results obtained from experiments, we found that PINNs could be an accurate output solution of SWE when its results were compared with the analytical method. In addition, PINNs also present better performance over the Artificial Neural Network. This study highlights the transformative potential of PINNs in revolutionizing water resources research, offering a new paradigm for accurate and efficient solutions to the SVE.

Keywords

Shallow water equations

Physics-informed neural networks

Artificial neural networks

천수방정식(shallow water equations, SWE)은 물의 거동을 수치적으로 해석하기 위한 지배방정식으로 수리수문 분야에 널리 활용되고 있으며, 비선형 연립방정식으로 일반적으로 수치적으로 해석할 수 있다. 하지만 기존의 여러 수치 해석법은 격자망 생성에 민감하며 복잡한 지형에서의 해석에 한계가 발생할 수 있다. 이러한 한계점을 극복하기 위하여 본 연구에서는 물리 정보 신경망(Physics-Informed Neural Networks, PINNs)을 사용하고자 하였다. PINNs은 물리 법칙을 신경망에 직접적으로 도입하여 지배방정식을 해석하고자 하는 기법이며 지배 방정식에 대한 물리적, 수학적 정보를 손실함수로 변환하여 최적화하고 해를 산정할 수 있다. 본 연구에서는 지배방정식을 PINNs 구조 내에서 사용할 수 있도록 신경망 구조, 학습 전략, 데이터 생성 기술과 같은 포괄적인 방법론을 제시하고 결과를 ANN 기법과 비교하였다. 물리적 사전지식이 반영되지 않은 ANN과 달리 PINNs은 천수방정식에 대하여 매우 정확한 수치적 솔루션을 효과적으로 제공하는 것으로 나타났다. 따라서 PINNs은 지배방정식의 수치해석적 연구에 많은 잠재력이 있는 것으로 판단되며, 정확하고 효율적인 천수방정식의 솔루션을 위한 기법으로 활용될 수 있을 것으로 기대된다.

키워드

천수방정식

물리 정보 신경망

인공신경망

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Information

Publisher :KOREA WATER RESOURECES ASSOCIATION
Publisher(Ko) :한국수자원학회
Journal Title :Journal of Korea Water Resources Association
Journal Title(Ko) :한국수자원학회 논문집
Volume : 56
No :12
Pages :939-953
Received Date : 2023-07-24
Revised Date : 2023-11-28
Accepted Date : 2023-11-30
DOI :https://doi.org/10.3741/JKWRA.2023.56.12.939

Journal of Korea Water Resources Association ISSN:2799-8746(Print) 2799-8754(Online) 한국수자원학회 논문집

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