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[SCG55-P14] Evaluation of Tsunami Propagation Using Physics Informed Neural Network (PINN)
Keywords:Machine learning , Physics Informed Neural Network, Tsunami
Forecast of Tsunami Propagation by Deep Learning
Toward the realization of tsunami propagation forecast by deep learning, tsunami forecasts performance was evaluated using numerical simulation data. This study aims to immediately forecast coastal tsunami waveforms at a future time from offshore observation data immediately after a tsunami occurs by learning CNN models for tsunami propagation at various tsunami sources. A general limitation of deep learning is that it is inaccurate for forecasts outside the range of the training dataset (extrapolated predictions), making long-range forecasts difficult. This study examines the feasibility of Physically Informed Neural Networks (PINN; Raissi et al. 2019) for extrapolation forecasts, by examines consistency with the tsunami equation in the training process. Rashet-Behesht et al. (2022) discussed in detail the feasibility of using PINN to forecast acoustic wave (P-wave) propagation and its application to velocity inversion, and Waheed et al. (2021) have successfully applied PINNto a real data of eikonal travel-time inversion of surface waves. This study draws on these previous studies to examine the applicability of PINN to the tsunami forecast problem.
Data and Method
The training dataset was created by a FDM simulation of the tsunami equation of a linear long wave model. Simulation area of 256 km x 192 km was discretized at 0.5 km intervals and tsunami propagation was calculated for 800 seconds from an initial wave source with a Gaussian distribution. Simulation results were thinning at 2 km intervals (128x96 grid points) to produce 200 snapshot images (Fig.1). The first 40 snapshots (160 sec) were used to train PINN, and then tsunami propagation forecasts were made for subsequent times (240, 360 and 480 sec). PINN was built using SciANN (Haghighat and Juanes 2021), a Wrapper in the Keras deep learning library, with a 4-layer model consisting of 40 neurons. The activation function was set to tanh, and the training was in the direction of minimizing the r.m.s. of the residuals between the tsunami forecast and the ground truth (simulation result) and the consistency between the estimated results (wave height and current velocity) and the tsunami equation. Here, the spatial and temporal derivatives of wave height and current velocity are obtained by an automatic differentiation function based on error back propagation of the PINN. The training of 2000 epochs with a batch size of 500 took 30 min. using GPU computation on a Wisteria supercomputer at the Information Technology Center, The University of Tokyo.
Tsunami Propagation Forecast Results
The tsunami propagation forecast using the trained PINN was completed in 0.05 seconds per forecast point and time by CPU calculation. The PINN forecast results show that the tsunami wavefront propagation is well reproduced even when the tsunami propagates outside of the training data (> 120 s) (Fig.2a). On the other hand, the ordinary CNN forecast, which does not use the tsunami equation as a constraint, shows a large outlier for the time outside the training data. Next, during the learning process of the long time (720 seconds) tsunami propagation by PINN, the bathymetry (sea depth) of the simulation model can be inverted as an unknown quantity in the tsunami equation (Fig.3).
Toward the realization of tsunami propagation forecast by deep learning, tsunami forecasts performance was evaluated using numerical simulation data. This study aims to immediately forecast coastal tsunami waveforms at a future time from offshore observation data immediately after a tsunami occurs by learning CNN models for tsunami propagation at various tsunami sources. A general limitation of deep learning is that it is inaccurate for forecasts outside the range of the training dataset (extrapolated predictions), making long-range forecasts difficult. This study examines the feasibility of Physically Informed Neural Networks (PINN; Raissi et al. 2019) for extrapolation forecasts, by examines consistency with the tsunami equation in the training process. Rashet-Behesht et al. (2022) discussed in detail the feasibility of using PINN to forecast acoustic wave (P-wave) propagation and its application to velocity inversion, and Waheed et al. (2021) have successfully applied PINNto a real data of eikonal travel-time inversion of surface waves. This study draws on these previous studies to examine the applicability of PINN to the tsunami forecast problem.
Data and Method
The training dataset was created by a FDM simulation of the tsunami equation of a linear long wave model. Simulation area of 256 km x 192 km was discretized at 0.5 km intervals and tsunami propagation was calculated for 800 seconds from an initial wave source with a Gaussian distribution. Simulation results were thinning at 2 km intervals (128x96 grid points) to produce 200 snapshot images (Fig.1). The first 40 snapshots (160 sec) were used to train PINN, and then tsunami propagation forecasts were made for subsequent times (240, 360 and 480 sec). PINN was built using SciANN (Haghighat and Juanes 2021), a Wrapper in the Keras deep learning library, with a 4-layer model consisting of 40 neurons. The activation function was set to tanh, and the training was in the direction of minimizing the r.m.s. of the residuals between the tsunami forecast and the ground truth (simulation result) and the consistency between the estimated results (wave height and current velocity) and the tsunami equation. Here, the spatial and temporal derivatives of wave height and current velocity are obtained by an automatic differentiation function based on error back propagation of the PINN. The training of 2000 epochs with a batch size of 500 took 30 min. using GPU computation on a Wisteria supercomputer at the Information Technology Center, The University of Tokyo.
Tsunami Propagation Forecast Results
The tsunami propagation forecast using the trained PINN was completed in 0.05 seconds per forecast point and time by CPU calculation. The PINN forecast results show that the tsunami wavefront propagation is well reproduced even when the tsunami propagates outside of the training data (> 120 s) (Fig.2a). On the other hand, the ordinary CNN forecast, which does not use the tsunami equation as a constraint, shows a large outlier for the time outside the training data. Next, during the learning process of the long time (720 seconds) tsunami propagation by PINN, the bathymetry (sea depth) of the simulation model can be inverted as an unknown quantity in the tsunami equation (Fig.3).