Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909651404062720 |
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| author | Kang, Ming Li, Hang Tan, Qiwen Wang, Zhan Li, Ruipeng Zhao, Junfang Xiang, Hui Fan, Dixia |
| author_facet | Kang, Ming Li, Hang Tan, Qiwen Wang, Zhan Li, Ruipeng Zhao, Junfang Xiang, Hui Fan, Dixia |
| contents | Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical constraints with data-driven optimization, PINNs overcome the critical challenges of parameter unmeasurability in the KdV equation for internal solitary waves in two-layer fluid systems. This work addresses two problems: (1) Operator learning constructs a mapping from parameters to solutions, enabling wave evolution predictions from unknown parameters. Comparative studies demonstrate prediction errors as low as $10^{-4}$ when using 1000 training points. (2) Inverse problem solving leverages sparse and potentially noisy observational data with physics-regularized constraints to invert nonlinear coefficients successfully. Compared to conventional approaches, this end-to-end differentiable paradigm unifies operator learning and inverse problem-solving while overcoming mesh discretization errors and high-dimensional parameter space iteration costs. The method shows effectiveness for internal wave problems in stratified fluids, providing both accurate forward modeling and robust parameter inversion capabilities, even under noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation Kang, Ming Li, Hang Tan, Qiwen Wang, Zhan Li, Ruipeng Zhao, Junfang Xiang, Hui Fan, Dixia Fluid Dynamics Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical constraints with data-driven optimization, PINNs overcome the critical challenges of parameter unmeasurability in the KdV equation for internal solitary waves in two-layer fluid systems. This work addresses two problems: (1) Operator learning constructs a mapping from parameters to solutions, enabling wave evolution predictions from unknown parameters. Comparative studies demonstrate prediction errors as low as $10^{-4}$ when using 1000 training points. (2) Inverse problem solving leverages sparse and potentially noisy observational data with physics-regularized constraints to invert nonlinear coefficients successfully. Compared to conventional approaches, this end-to-end differentiable paradigm unifies operator learning and inverse problem-solving while overcoming mesh discretization errors and high-dimensional parameter space iteration costs. The method shows effectiveness for internal wave problems in stratified fluids, providing both accurate forward modeling and robust parameter inversion capabilities, even under noise. |
| title | Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2506.14236 |