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Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to…

Machine Learning · Computer Science 2024-01-29 Yongsheng Mei , Mahdi Imani , Tian Lan

Inverse problems governed by partial differential equations (PDEs) play a crucial role in various fields, including computational science, image processing, and engineering. Particularly, Darcy flow equation is a fundamental equation in…

Machine Learning · Statistics 2025-07-24 Hongji Wang , Hongqiao Wang , Jinyong Ying , Qingping Zhou

This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…

Machine Learning · Statistics 2025-08-18 Jinwen Xu , Qin Lu , Yaakov Bar-Shalom

A plethora of applications entail solving black-box optimization problems with high evaluation costs, including drug discovery, material design, as well as hyperparameter tuning. Toward finding the global optimum of such black-box…

Machine Learning · Computer Science 2025-10-06 Haotian Xiang , Jinwen Xu , Qin Lu

Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation…

Optimization and Control · Mathematics 2021-06-14 L. Jeff Hong , Xiaowei Zhang

Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…

The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by…

Computation · Statistics 2013-04-17 John Geweke , Garland Durham , Huaxin Xu

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

Computation · Statistics 2022-08-18 Oskar Gustafsson , Mattias Villani , Pär Stockhammar

Bayesian Optimization (BO) has been widely used to efficiently optimize expensive black-box functions with limited evaluations. In this paper, we investigate the use of BO for prompt engineering to enhance text classification with Large…

Artificial Intelligence · Computer Science 2025-10-17 Adam Ballew , Jingbo Wang , Shaogang Ren

Bayesian optimization (BO) methods often rely on the assumption that the objective function is well-behaved, but in practice, this is seldom true for real-world objectives even if noise-free observations can be collected. Common approaches,…

Machine Learning · Statistics 2020-09-10 Erik Bodin , Markus Kaiser , Ieva Kazlauskaite , Zhenwen Dai , Neill D. F. Campbell , Carl Henrik Ek

Learning controller parameters from closed-loop data has been shown to improve closed-loop performance. Bayesian optimization, a widely used black-box and sample-efficient learning method, constructs a probabilistic surrogate of the…

Machine Learning · Computer Science 2025-12-15 Sebastian Hirt , Valentinus Suwanto , Hendrik Alsmeier , Maik Pfefferkorn , Rolf Findeisen

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…

Machine Learning · Computer Science 2020-03-31 George De Ath , Richard M. Everson , Jonathan E. Fieldsend , Alma A. M. Rahat

Tailoring the functional properties of advanced organic/inorganic heterogeonous devices to their intended technological applications requires knowledge and control of the microscopic structure inside the device. Atomistic quantum mechanical…

Materials Science · Physics 2019-03-13 Milica Todorović , Michael U. Gutmann , Jukka Corander , Patrick Rinke

The surrogate-assisted optimization algorithm is a promising approach for solving expensive multi-objective optimization problems. However, most existing surrogate-assisted multi-objective optimization algorithms have three main drawbacks:…

Neural and Evolutionary Computing · Computer Science 2018-11-06 Xi Lin , Hui-Ling Zhen , Zhenhua Li , Qingfu Zhang , Sam Kwong

The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is…

Machine Learning · Statistics 2020-08-07 Marko Järvenpää , Aki Vehtari , Pekka Marttinen

Bayesian optimization (BO) is a widely used method for data-driven optimization that generally relies on zeroth-order data of objective function to construct probabilistic surrogate models. These surrogates guide the…

Machine Learning · Computer Science 2025-08-08 Georgios Makrygiorgos , Joshua Hang Sai Ip , Ali Mesbah

Parameter calibration is essential for reducing uncertainty and improving predictive fidelity in physics-based models, yet it is often limited by the high computational cost of model evaluations. Bayesian calibration methods provide a…

Methodology · Statistics 2026-01-21 Maike F. Holthuijzen , Atlanta Chakraborty , Elizabeth Krath , Tommie Catanach

In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact,…

Machine Learning · Computer Science 2025-09-26 Hanyang Wang , Juergen Branke , Matthias Poloczek

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

Numerical Analysis · Mathematics 2025-03-19 Shane A. McQuarrie , Anirban Chaudhuri , Karen E. Willcox , Mengwu Guo

A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…

Methodology · Statistics 2015-09-29 Tiep Mai , Simon Wilson