Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks
Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties and challenges. In this study, we propose a method utilizin...
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MDPI AG
2025-01-01
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| Series: | Computation |
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| author | Van Truong Vo Samad Noeiaghdam Denis Sidorov Aliona Dreglea Liguo Wang |
| author_facet | Van Truong Vo Samad Noeiaghdam Denis Sidorov Aliona Dreglea Liguo Wang |
| author_sort | Van Truong Vo |
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| description | Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties and challenges. In this study, we propose a method utilizing Physics-Informed Neural Networks (PINNs) to solve the nonlinear energy supply–demand (ESD) system. We design a neural network with four outputs, where each output approximates a function that corresponds to one of the unknown functions in the nonlinear system of differential equations describing the four-dimensional ESD problem. The neural network model is then trained, and the parameters are identified and optimized to achieve a more accurate solution. The solutions obtained from the neural network for this problem are equivalent when we compare and evaluate them against the Runge–Kutta numerical method of order 5(4) (RK45). However, the method utilizing neural networks is considered a modern and promising approach, as it effectively exploits the superior computational power of advanced computer systems, especially in solving complex problems. Another advantage is that the neural network model, after being trained, can solve the nonlinear system of differential equations across a continuous domain. In other words, neural networks are not only trained to approximate the solution functions for the nonlinear ESD system but can also represent the complex dynamic relationships between the system’s components. However, this approach requires significant time and computational power due to the need for model training. Furthermore, as this method is evaluated based on experimental results, ensuring the stability and convergence speed of the model poses a significant challenge. The key factors influencing this include the manner in which the neural network architecture is designed, such as the selection of hyperparameters and appropriate optimization functions. This is a critical and highly complex task, requiring experimentation and fine-tuning, which demand substantial expertise and time. |
| format | Article |
| id | doaj-art-cd25d8f703284b24a84bf25aabb39130 |
| institution | Kabale University |
| issn | 2079-3197 |
| language | English |
| publishDate | 2025-01-01 |
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| series | Computation |
| spelling | doaj-art-cd25d8f703284b24a84bf25aabb391302025-01-24T13:27:48ZengMDPI AGComputation2079-31972025-01-011311310.3390/computation13010013Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural NetworksVan Truong Vo0Samad Noeiaghdam1Denis Sidorov2Aliona Dreglea3Liguo Wang4Scientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, RussiaInstitute of Mathematics, Henan Academy of Sciences, Zhengzhou 450046, ChinaScientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, RussiaScientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, RussiaSchool of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, ChinaNonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties and challenges. In this study, we propose a method utilizing Physics-Informed Neural Networks (PINNs) to solve the nonlinear energy supply–demand (ESD) system. We design a neural network with four outputs, where each output approximates a function that corresponds to one of the unknown functions in the nonlinear system of differential equations describing the four-dimensional ESD problem. The neural network model is then trained, and the parameters are identified and optimized to achieve a more accurate solution. The solutions obtained from the neural network for this problem are equivalent when we compare and evaluate them against the Runge–Kutta numerical method of order 5(4) (RK45). However, the method utilizing neural networks is considered a modern and promising approach, as it effectively exploits the superior computational power of advanced computer systems, especially in solving complex problems. Another advantage is that the neural network model, after being trained, can solve the nonlinear system of differential equations across a continuous domain. In other words, neural networks are not only trained to approximate the solution functions for the nonlinear ESD system but can also represent the complex dynamic relationships between the system’s components. However, this approach requires significant time and computational power due to the need for model training. Furthermore, as this method is evaluated based on experimental results, ensuring the stability and convergence speed of the model poses a significant challenge. The key factors influencing this include the manner in which the neural network architecture is designed, such as the selection of hyperparameters and appropriate optimization functions. This is a critical and highly complex task, requiring experimentation and fine-tuning, which demand substantial expertise and time.https://www.mdpi.com/2079-3197/13/1/13nonlinear energy supply and demand systemphysics-informed neural networksmachine learningdeep learningnumerical method |
| spellingShingle | Van Truong Vo Samad Noeiaghdam Denis Sidorov Aliona Dreglea Liguo Wang Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks Computation nonlinear energy supply and demand system physics-informed neural networks machine learning deep learning numerical method |
| title | Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks |
| title_full | Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks |
| title_fullStr | Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks |
| title_full_unstemmed | Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks |
| title_short | Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks |
| title_sort | solving nonlinear energy supply and demand system using physics informed neural networks |
| topic | nonlinear energy supply and demand system physics-informed neural networks machine learning deep learning numerical method |
| url | https://www.mdpi.com/2079-3197/13/1/13 |
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