Estimation of Open Boundary Conditions for an Internal Tidal Model with Adjoint Method: A Comparative Study on Optimization Methods

Abstract

Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS) method and two gradient descent (GD) methods (the normal one with Wolfe’s line search and the simplified one) are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs) are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.

Trajectory Estimation of Aircraft in a Double-Satellite Passive Positioning System with the Adjoint Method

“…wherẽ,̃,̃and , , are prior and optimized values, receptively. Because the values of cost function decrease along the opposite direction of the gradient, by employing typical steepest descent method [11], , , and can be optimized during iterations.…”

Adjoint-based calibration of inlet boundary condition for atmospheric computational fluid dynamics solvers

“…Using the measurement data and an inverse analysis, the unknown BCs can be obtained with an optimization algorithm. This approach is called open boundary optimization and has been successfully tried in oceanography (Seiler, 1993;Chen et al, 2013) and numerical wind prediction (NWP) models (Schneiderbauer and Pirker, 2011). Another approach is to use observations and statistical analysis (Glover et al, 2011) to calibrate the CFD model parameters (e.g., inflow and turbulence model constants).…”

“…The solution to an optimization problem can be found with different methods. However, the methods such as genetic algorithm and evolutionary strategies (Davis, 1991;Michalewicz, 1996) require a large number of function evaluations which in CFD applications can be computationally very expensive. Alternatively, the gradient-based optimizers (Ruder, 2016) use the derivative of cost function with respect to the design parameters.…”

Adjoint-based Calibration of Inlet Boundary Condition for Atmospheric CFD Solvers

“…Using the measurement data and an inverse analysis, the unknown BCs can be obtained with an optimization algorithm. This approach is called open boundary optimization and has been successfully tried in oceanography (Seiler, 1993;Chen et al, 2013) and numerical wind prediction (NWP) models (Schneiderbauer and Pirker, 2011). Another approach is to use observations and statistical analysis (Glover et al, 2011) to calibrate the CFD model parameters (e.g., inflow and turbulence model constants) .…”