Related papers: Optimal Bayesian experimental design for subsurfac…
Bayesian optimization provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g. in machine learning to optimize…
We propose the combination of forward shape derivatives and the use of an iterative inversion scheme for Bayesian optimization to find optimal designs of nanophotonic devices. This approach widens the range of applicability of Bayesian…
Optimal design for linear regression is a fundamental task in statistics. For finite design spaces, recent progress has shown that random designs drawn using proportional volume sampling (PVS) lead to approximation guarantees for A-optimal…
Bayesian design can be used for efficient data collection over time when the process can be described by the solution to an ordinary differential equation (ODE). Typically, Bayesian designs in such settings are obtained by maximising the…
Sequential Bayesian optimal experimental design (SBOED) for PDE-governed inverse problems is computationally challenging, especially for infinite-dimensional random field parameters. High-fidelity approaches require repeated forward and…
The paper addresses Bayesian inferences in inverse problems with uncertainty quantification involving a computationally expensive forward map associated with solving a partial differential equations. To mitigate the computational cost, the…
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic.…
Solving large-scale capacity expansion problems (CEPs) is central to cost-effective decarbonization of regional-scale energy systems. To ensure the intended outcomes of CEPs, modeling uncertainty due to weather-dependent variable renewable…
Bayesian Optimization is a very effective tool for optimizing expensive black-box functions. Inspired by applications developing and characterizing reaction chemistry using droplet microfluidic reactors, we consider a novel setting where…
Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…
Design optimisation potentially leads to lightweight aircraft structures with lower environmental impact. Due to the high number of design variables and constraints, these problems are ordinarily solved using gradient-based optimisation…
The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…
Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…
We propose a new procedure named PASOA, for Bayesian experimental design, that performs sequential design optimization by simultaneously providing accurate estimates of successive posterior distributions for parameter inference. The…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
We consider infinite-dimensional Bayesian linear inverse problems governed by time-dependent partial differential equations (PDEs) and develop a mathematical and computational framework for optimal design of mobile sensor paths in this…