Efficient methods for large-scale PDE-constrained optimization in the presence of uncertainty and complex technological constraints

Optimization problems constrained by partial differential equations (PDEs) are ubiquitous in engineering. These problems emerge in design optimization, when relying upon a high-fidelity high-dimensional representation of the underlying physics by means of a system of PDEs. Today, the main challenges of PDE-constrained optimization for engineering are: (1) the excessive computational cost of the PDE-solution during the iterative optimization process, (2) the need to take uncertainty into account, so that designs are robust, and (3) complex technological constraints. In the current project, we develop novel multi-grid, multi-level, and multi-fidelity methods for PDE-constrained optimization algorithms, with focus on gradient-based optimization using adjoint techniques. This will allow us to advance the state-of-the-art in cutting-edge engineering problems such as wind-farm control and design, divertor design in nuclear fusion tokamaks, heat-sink design, environmental ground vibration, and structural engineering.

Keywords:constraints

Disciplines:Design theories and methods, Mechanics, Other mechanical and manufacturing engineering