Active learning for feasible region discovery

Often in the design process of an engineer, the design specifications of the system are not completely known initially. However, usually there are some physical constraints which are already known, corresponding to a region of interest in the design space that is called feasible. These constraints often have no analytical form but need to be characterised based on expensive simulations or measurements. Therefore, it is important that the feasible region can be modeled sufficiently accurate using only a limited amount of samples. This can be solved by using active learning techniques that minimize the amount of samples w.r.t. what we try to model. Most active learning strategies focus on classification models or regression models with classification accuracy and regression accuracy in mind respectively. In this work, regression models of the constraints are used, but only the (in) feasibility is of interest. To tackle this problem, an information-theoretic sampling strategy is constructed to discover these regions. The proposed method is then tested on two synthetic examples and one engineering example and proves to outperform the current state-of-the-art

Stochastic collocation on unstructured multivariate meshes

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications. Selection of a collocation mesh is frequently a challenge, but methods that construct geometrically "unstructured" collocation meshes have shown great potential due to attractive theoretical properties and direct, simple generation and implementation. We investigate properties of these meshes, presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure