State and parameter identification of linearized water wave equation via adjoint method

In this paper, we focus on the state and parameter identification problem of a hydrodynamical system. This system is modeled as a linearized water wave equation(LWWE), a hyperbolic state-space model coupled with a Laplace equation. We assume that the wave elevation at two distinct points is the only measurement of water waves. We show that the state and water depth can be reconstructed from this point measurement records. The identification problem is recast as an optimization problem over an infinite-dimensional space. We propose the adjoint method-based identification algorithm to generate an estimated state and water depth. We then performed a numerical simulation to show the effectiveness of our designed algorithm by comparing it with existing studies.