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Neural networks are powerful surrogates for numerous forward processes. The inversion of such surrogates is extremely valuable in science and engineering. The most important property of a successful neural inverse method is the performance…

Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This can be formulated as parametric expensive multi-objective optimization problems…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples…

This paper addresses the integration of additional information sources into a Bayesian optimization framework while ensuring that safety constraints are satisfied. The interdependencies between these information sources are modeled using an…

We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

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…

This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…

Bayesian inverse problems arise in various scientific and engineering domains, and solving them can be computationally demanding. This is especially the case for problems governed by partial differential equations, where the repeated…

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…

Several scenarios require the optimization of non-convex black-box functions, that are noisy expensive to evaluate functions with unknown analytical expression, whose gradients are hence not accessible. For example, the hyper-parameter…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…

Experimental (design) optimization is a key driver in designing and discovering new products and processes. Bayesian Optimization (BO) is an effective tool for optimizing expensive and black-box experimental design processes. While Bayesian…

In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

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…

The use of transfer learning within Bayesian optimization addresses the disadvantages of the so-called \textit{cold start} problem by using source data to aid in the optimization of a target problem. We present a method that leverages an…