Algorithms for the numerical solution of optimization problems with time-dependent PDEs are computationally extremely demanding, as they require multiple PDE solves during the iterative optimization process. With today's modern computers, the time-to-solution can be decreased through massive parallelization, which is traditionally done in the spatial dimensions, but more recently also in the...
Many physics-informed data integrated modeling approaches require the solution of optimization problems with evolutionary constraints. This talk develops scalable algorithms for transient PDE-constrained optimization. Here, simulation-based optimization repeatedly executes the simulator’s forward and adjoint time integration schemes. Consequently, the arrow of time creates a sequential...
In recent years, multiple shooting methods have found their way from simple ODE-based optimization to tackling more intricate, moderate to large-scale PDE-based problems. By fully exploiting the multiple shooting paradigm through parallel-in-time integration of the shooting windows, it may allow for substantial parallel speed-ups, thereby accelerating the convergence of the optimization. This...
PDE-constrained optimization problems arise in various applications in industry and can also be useful in other mathematical fields. Applications can be found in physics, chemistry, biology, medical imaging, optimal transport, and many other areas. Due to the lack of analytical solutions to these problems in general, the fast and robust numerical solution is of utmost importance. However, the...
This talk will introduce a new diagonalization technique for the parallel-in-time solution of linear-quadratic optimal control problems with time-invariant system matrices. The target problems are often derived from a semi-discretization of a Partial Differential Equation (PDE)-constrained optimization problem. The solution of large-scale time dependent optimal control problems is...
For the prediction and study of water flows in a river or channel the knowledge of the bottom topography - the bathymetry - is required. Direct measurements of bathymetries are possible, but can be very expensive and time consuming. This motivates the development of methods to reconstruct a bathymetry numerically. In this talk, an approach will be shown that uses measurements of the water...
