Scholarlink

<p>Tsunami wave dynamics are inherently nonlinear and dispersive, making them challenging to model using conventional techniques. To address this, the present work develops a physics-informed Least Squares Support Vector Machine (PILSSVM) framework for approximating solutions of the geophysical Korteweg–de Vries (GeoKdV) equation, which describes long-wave propagation in equatorial regions. The proposed approach incorporates the governing partial differential equation along with initial and boundary conditions directly into the learning process, ensuring physical consistency and solution accuracy. The GeoKdV equation is considered as a benchmark problem to systematically validate the performance of the proposed framework under controlled conditions. For comparison, several data-driven models, including Support Vector Machine (SVM), Gaussian Process Regression (GPR), Multi-Layer Perceptron (MLP), Random Forest (RF), and Extreme Learning Machine (ELM), are also implemented to illustrate the distinction between data-driven and physics-informed learning. In addition, kernel function analysis (RBF, Laplacian, Polynomial, and Linear) is conducted to examine their influence on approximation accuracy and PDE residuals. The effect of key physical parameters, namely the Coriolis parameter and wave velocity, is analyzed to assess the capability of the proposed framework to capture the parametric dependence of the wave profile. Hyperparameter sensitivity and PDE residual analysis are further performed to evaluate training stability and solution consistency. The results demonstrate that the proposed physics-informed formulation provides stable and physically consistent approximations under varying modeling conditions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Kernel-based physics-informed machine learning model for nonlinear tsunami wave evolution under dispersive dynamics with parameter-dependent behaviours

  • 期刊论文

  • 发表日期：

    2026年5月19日

查看全文
  • Bhubaneswari Mishra,
  • Mrutyunjaya Sahoo,
  • S. Chakraverty

摘要

Tsunami wave dynamics are inherently nonlinear and dispersive, making them challenging to model using conventional techniques. To address this, the present work develops a physics-informed Least Squares Support Vector Machine (PILSSVM) framework for approximating solutions of the geophysical Korteweg–de Vries (GeoKdV) equation, which describes long-wave propagation in equatorial regions. The proposed approach incorporates the governing partial differential equation along with initial and boundary conditions directly into the learning process, ensuring physical consistency and solution accuracy. The GeoKdV equation is considered as a benchmark problem to systematically validate the performance of the proposed framework under controlled conditions. For comparison, several data-driven models, including Support Vector Machine (SVM), Gaussian Process Regression (GPR), Multi-Layer Perceptron (MLP), Random Forest (RF), and Extreme Learning Machine (ELM), are also implemented to illustrate the distinction between data-driven and physics-informed learning. In addition, kernel function analysis (RBF, Laplacian, Polynomial, and Linear) is conducted to examine their influence on approximation accuracy and PDE residuals. The effect of key physical parameters, namely the Coriolis parameter and wave velocity, is analyzed to assess the capability of the proposed framework to capture the parametric dependence of the wave profile. Hyperparameter sensitivity and PDE residual analysis are further performed to evaluate training stability and solution consistency. The results demonstrate that the proposed physics-informed formulation provides stable and physically consistent approximations under varying modeling conditions.