ICCE 2022

How to Cite

PHYSICS-INFORMED DEEP LEARNING OF NEARSHORE WAVE PROCESSES. (2023). Coastal Engineering Proceedings, 37, papers.14.


The paper introduces the NWnets, a physics-informed deep learning model for reconstructing nearshore wave fields and mapping bathymetry. The physics encoded into the deep neural networks are the wave energy balance equation and dispersion relation. Insights into the model capability are gained through application of the NWnets to a laboratory experiment of wave transformation over a circular shoal. If the bathymetry and discrete measurements of wave height are available, the NWnets model is capable of simulating nearshore wave transformation. Moreover, the extended NWnets can be used for depth inversion if the bathymetry is unknown. Two methods for simultaneously estimating water depths and surface waves are presented. If surface wave number and limited wave height measurements are available from remote sensing platforms, the first method employs wave numbers and scarce measurements of wave height as training data. The second method utilizes scarce wave height and limited water depth measurements as training points to reconstruct bathymetry and wave fields. The results show that both methods are capable of simultaneously mapping the bathymetry and waves when the locations of training points are appropriately distributed.


Chawla, A.K., Kirby, J.T., 1996. Wave transformation over a submerged shoal. University of

Delaware, Dept. of Civil Engineering, Center for Applied Coastal Research, Newark, Del.

Chen, Q., Kirby, J.T., Dalrymple, R.A., Shi, F., Thornton, E.B., 2003. Boussinesq modeling of

longshore currents. J. Geophys. Res. Ocean. 108.

Chen, Q., Wang, N., and Chen, Z., 2023. Simultaneous mapping of nearshore bathymetry and waves

based on physics-informed deep learning. Coastal Engineering, under review.

Chen, Z., Liu, Y., Sun, H., 2021. Physics-informed learning of governing equations from scarce data.

Nat. Commun. 12, 1–13.

Gao, H., Sun, L., Wang, J.-X., 2021. Super-resolution and denoising of fluid flow using physicsinformed

convolutional neural networks without high-resolution labels. Phys. Fluids 33, 73603.

Grilli, S. 1998. Depth inversion in shallow water based on nonlinear properties of shoaling periodic

waves. Coast. Eng. 35 (3), 185-209.

Janssen, T.T., Battjes, J.A., 2007. A note on wave energy dissipation over steep beaches. Coast. Eng.

, 711–716.

Jin, X., Cai, S., Li, H., Karniadakis, G.E., 2021. NSFnets (Navier-Stokes flow nets): Physicsinformed

neural networks for the incompressible Navier-Stokes equations. J. Comput. Phys.

, 109951.

Karniadakis, G.E., Kevrekidis, I.G., Lu, L., Perdikaris, P., Wang, S., Yang, L., 2021. Physicsinformed

machine learning. Nat. Rev. Phys. 3, 422–440.

Kirby, J.T., Dalrymple, R.A., 1986. An approximate model for nonlinear dispersion in

monochromatic wave propagation models. Coast. Eng. 9, 545–561.

Kissas, G., Yang, Y., Hwuang, E., Witschey, W.R., Detre, J.A., Perdikaris, P., 2020. Machine

learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive

D flow MRI data using physics-informed neural networks. Comput. Methods Appl. Mech.

Eng. 358, 112623.

Lu, L., Meng, X., Mao, Z., Karniadakis, G.E., 2021. DeepXDE: A deep learning library for solving

differential equations. SIAM Rev. 63, 208–228.

Raissi, M., Wang, Z., Triantafyllou, M.S., Karniadakis, G.E., 2019. Deep learning of vortex-induced

vibrations. J. Fluid Mech. 861, 119–137.

Roelvink, D., Reniers, A., Van Dongeren, A.P., De Vries, J.V.T., McCall, R., Lescinski, J., 2009.

Modelling storm impacts on beaches, dunes and barrier islands. Coast. Eng. 56, 1133–1152.

Sun, L., Gao, H., Pan, S., Wang, J.-X., 2020. Surrogate modeling for fluid flows based on physicsconstrained

deep learning without simulation data. Comput. Methods Appl. Mech. Eng. 361,

Wang, N., Chen, Q., Chen, Z., 2022. Reconstruction of nearshore wave fields based on physicsinformed

neural networks. Coast. Eng. 104167.

Wilson, G.W., Özkan-Haller, H.T., Holman, R.A., Haller, M.C., Honegger, D.A., Chickadel, C.C.,

Surf zone bathymetry and circulation predictions via data assimilation of remote sensing

observations. J. Geophys. Res. Ocean. 119, 1993–2016.

Yoo, J., Fritz, H.M., Haas, K.A., Work, P.A., Barnes, C.F., 2011. Depth inversion in the surf zone

with inclusion of wave nonlinearity using video-derived celerity. J. Waterw. Port, Coast. Ocean

Eng. 137, 95–106.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright (c) 2023 Qin Chen, Nan Wang, Zhao Chen