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

srMO-BO-3GP: A sequential regularized multi-objective constrained Bayesian optimization for design applications

Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including multi-objective, multi-fidelity, parallelization, latent-variable model, have been proposed to improve the limitation of the classical BO framework. In this work, we propose a novel multi-objective (MO) extension, called srMO-BO-3GP, to solve the MO optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each of the GP is assigned with a different task: the first GP is used to approximate the single-objective function, the second GP is used to learn the unknown constraints, and the third GP is used to learn the uncertain Pareto frontier. At each iteration, a MO augmented Tchebycheff function converting MO to single-objective is adopted and extended with a regularized ridge term, where the regularization is introduced to smoothen the single-objective function. Finally, we couple the third GP along with the classical BO framework to promote the richness and diversity of the Pareto frontier by the exploitation and exploration acquisition function. The proposed framework is demonstrated using several numerical benchmark functions, as well as a thermomechanical finite element model for flip-chip package design optimization