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The fundamental computational issues in Bayesian inverse problems (BIP) governed by partial differential equations (PDEs) stem from the requirement of repeated forward model evaluations. A popular strategy to reduce such costs is to replace…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…
Many control problems require repeated tuning and adaptation of controllers across distinct closed-loop tasks, where data efficiency and adaptability are critical. We propose a hierarchical Bayesian optimization (BO) framework that is…
By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…
We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…
Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat\'ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based…
We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent…
We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our…
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…
Data collected by the Interstellar Boundary Explorer (IBEX) satellite, recording heliospheric energetic neutral atoms (ENAs), exhibit a phenomenon that has caused space scientists to revise hypotheses about the physical processes, and…
Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…
Bayesian Optimization (BO) methods are useful for optimizing functions that are expen- sive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the…
Automated chemical synthesis, materials fabrication, and spectroscopic physical measurements often bring forth the challenge of process trajectory optimization, i.e., discovering the time dependence of temperature, electric field, or…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
Bayesian Optimization (BO) is a data-driven strategy for minimizing/maximizing black-box functions based on probabilistic surrogate models. In the presence of safety constraints, the performance of BO crucially relies on tight probabilistic…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…