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<p>A partial differential equation (PDE)-based approach combines soliton theory with data-driven and physics-constrained training to probe solitary wave dynamics and shoaling-induced amplification. A comparison of two advanced deep learning approaches, fully connected neural networks (FCNs) and physics-informed neural networks (PINNs), demonstrates distinct trade-offs among predictive accuracy, computational efficiency, and physical consistency. By explicitly incorporating governing physical laws into the training process, Such PINNs impose governing physical constraints that markedly improve extrapolation at significantly higher cost, where FCNs have superior accuracy and computational efficiency. These findings provide practical criteria for selecting appropriate deep learning strategies for complex wave modeling applications. From a geophysical perspective, the <i>variable-coefficient KdV equation</i> is employed as an idealized surrogate to expose bathymetry-driven shoaling and nonlinear energy focusing in tsunami-like wave evolution. The results further reinforce the established physical understanding that variations in bathymetric amplitude and abrupt topographic changes strongly influence wave generation, propagation, and amplification in deep-ocean environments. Overall, the findings position physics-aware deep learning as a decisive and scalable paradigm for physically grounded environmental wave analysis and predictive modeling.</p>

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A conceptual link to long-wave and tsunami-like events using neural networks

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • N. Hemnath,
  • Sandip Saha,
  • Santanu Raut

摘要

A partial differential equation (PDE)-based approach combines soliton theory with data-driven and physics-constrained training to probe solitary wave dynamics and shoaling-induced amplification. A comparison of two advanced deep learning approaches, fully connected neural networks (FCNs) and physics-informed neural networks (PINNs), demonstrates distinct trade-offs among predictive accuracy, computational efficiency, and physical consistency. By explicitly incorporating governing physical laws into the training process, Such PINNs impose governing physical constraints that markedly improve extrapolation at significantly higher cost, where FCNs have superior accuracy and computational efficiency. These findings provide practical criteria for selecting appropriate deep learning strategies for complex wave modeling applications. From a geophysical perspective, the variable-coefficient KdV equation is employed as an idealized surrogate to expose bathymetry-driven shoaling and nonlinear energy focusing in tsunami-like wave evolution. The results further reinforce the established physical understanding that variations in bathymetric amplitude and abrupt topographic changes strongly influence wave generation, propagation, and amplification in deep-ocean environments. Overall, the findings position physics-aware deep learning as a decisive and scalable paradigm for physically grounded environmental wave analysis and predictive modeling.