A GPU accelerated adjoint-based optimizer for inverse modeling of the two-dimensional shallow water equations

The increasing computational capacity of current computing technologies makes feasible the application of predictive high-resolution mathematical models for studying physical phenomena. Additionally, this can be enhanced if those methods are incorporated to some optimization method in order to perform inverse modeling. In this paper, an optimization procedure based on the adjoint equations is used for the reconstruction of information in a 2D Shallow Water model previously developed and proved to be fast, robust and accurate. The continuous adjoint approach used for the evaluation of the gradient that is introduced in a gradient-based optimizer. Furthermore, the computation of both physical and adjoint systems is accelerated by the use of GPU programming. Even though notable speed-ups are achieved with this technique they are only possible in small to medium size grids due to memory limitations. A novel checkpointing strategy is proposed to allow data handling in these devices hence offering the possibility to overcome that limitation.