Real-time optimization using proper orthogonal decomposition: Free surface shape prediction due to underwater bubble dynamics

A new data-driven reduced-order modeling approach for real-time optimization applications is presented. The proper orthogonal decomposition (POD) technique is used for the reduced-order model, with the basis functions determined from an ensemble of offline high-fidelity simulations. For optimization in real time, a rapid two-stage approach is taken in the online phase: the POD coefficients are first determined by solving a small optimization problem, and the desired parameters are subsequently obtained by interpolation of the POD coefficients using precomputed information from the simulation ensemble. This method is applied to optimizing parameters for underwater bubble explosions so that a desired free surface shape is generated. For time-critical applications, such as using the water barrier generated to stop sea-skimming objects, the time available for online optimization is limited to about 30 s. Results for two-dimensional simulation, using a personal computer (dual CPU running at 2.8 GHz), show that our new methodology is able to meet such a critical time requirement. For three-dimensional simulations, the time taken for computation increases, and a faster computer or parallel implementation is required.