Existing solvers for nonlinear, spatio-temporal fractional tsunami equations converge slowly and scale poorly. This study aims to propose a hybrid physics-informed framework, ConvLSTMbased Fractional-order Physics-Informed Wavelet Neural Network (L-FPWNN), to raise accuracy and stability, offering more reliable early-warning support for coastal disaster mitigation.
L-FPWNN couples a convolutional long short-term memory network (ConvLSTM) backbone with a physics-informed neural network (PINN). Spatial derivatives are obtained by automatic differentiation, whereas Caputo time-fractional terms are discretized via an L1 scheme. Initial and boundary conditions are enforced through tensor masking. An adaptive loss balancer and a cosine-annealed learning rate guide training over 11,000 Adam iterations on a CPU-only platform.
On benchmark fractional tsunami-wave tests, L-FPWNN lowers the u-component’s maximum absolute error from 0.005263 (baseline PINN) to 0.001442 within the [0,1] domain, maintaining level accuracy across all grid points. The model converges faster and with greater numerical stability than competing approaches.
This work presents the first ConvLSTM-enhanced PINN for time-fractional coupled partial differential equations, delivering a physically consistent, high-precision solution strategy that generalizes to large-scale spatio-temporal problems. Its efficiency and reliability make it attractive for geophysical forecasting and other complex fractional systems.
