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Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…

Machine Learning · Statistics 2025-05-15 O. Deniz Akyildiz , Mark Girolami , Andrew M. Stuart , Arnaud Vadeboncoeur

Inverse problems are the task of calibrating models to match data. They play a pivotal role in diverse engineering applications by allowing practitioners to align models with reality. In many applications, engineers and scientists do not…

Machine Learning · Computer Science 2026-03-05 Pengyu Zhang , Arnaud Vadeboncoeur , Alex Glyn-Davies , Mark Girolami

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of…

Numerical Analysis · Mathematics 2024-02-22 Daniel Sanz-Alonso , Nathan Waniorek

We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the…

Numerical Analysis · Mathematics 2020-10-22 Sebastian Lunz , Andreas Hauptmann , Tanja Tarvainen , Carola-Bibiane Schönlieb , Simon Arridge

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…

Numerical Analysis · Mathematics 2020-03-03 Liang Yan , Tao Zhou

The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which…

Artificial Intelligence · Computer Science 2012-02-20 James Cussens

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…

Computational Engineering, Finance, and Science · Computer Science 2023-12-14 Maximilian Dinkel , Carolin M. Geitner , Gil Robalo Rei , Jonas Nitzler , Wolfgang A. Wall

Machine Learning surrogates have been developed to accelerate solving systems dynamics of complex processes in different science and engineering applications. To faithfully capture governing systems dynamics, these methods rely on large…

Machine Learning · Computer Science 2025-07-01 Amir Hossein Rahmati , Nathan M. Urban , Byung-Jun Yoon , Xiaoning Qian

We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of…

Machine Learning · Statistics 2017-11-02 Young Woong Park , Diego Klabjan

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…

Optimization and Control · Mathematics 2026-01-12 Kaichen Shen , Peng Chen

In industrial machine learning pipelines, data often arrive in parts. Particularly in the case of deep neural networks, it may be too expensive to train the model from scratch each time, so one would rather use a previously learned model…

Machine Learning · Statistics 2018-03-29 Max Kochurov , Timur Garipov , Dmitry Podoprikhin , Dmitry Molchanov , Arsenii Ashukha , Dmitry Vetrov

We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…

Numerical Analysis · Mathematics 2017-11-17 Alen Alexanderian , Arvind K. Saibaba

We consider the problem of learning Bayesian networks (BNs) from complete discrete data. This problem of discrete optimisation is formulated as an integer program (IP). We describe the various steps we have taken to allow efficient solving…

Artificial Intelligence · Computer Science 2015-03-24 Mark Bartlett , James Cussens

One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…

Statistics Theory · Mathematics 2021-01-08 Neil K. Chada , Claudia Schillings , Xin T. Tong , Simon Weissmann

Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B${}^{-1}$, an inverse basis-to-basis neural operator framework that…

Machine Learning · Computer Science 2025-12-23 Adam J. Thorpe , Stepan Tretiakov , Dibakar Roy Sarkar , Krishna Kumar , Ufuk Topcu

Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…

Systems and Control · Electrical Eng. & Systems 2024-12-03 Zhexuan Zeng , Ruikun Zhou , Yiming Meng , Jun Liu

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

Machine Learning · Computer Science 2026-02-03 Shao-Ting Chiu , Aditya Nambiar , Ali Syed , Jonathan W. Siegel , Ulisses Braga-Neto

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…

Machine Learning · Computer Science 2024-05-30 Benjamin Shih , Ahmad Peyvan , Zhongqiang Zhang , George Em Karniadakis

Controller tuning and parameter optimization are crucial in system design to improve closed-loop system performance. Bayesian optimization has been established as an efficient model-free controller tuning and adaptation method. However,…

Systems and Control · Electrical Eng. & Systems 2024-04-24 Christopher König , Raamadaas Krishnadas , Efe C. Balta , Alisa Rupenyan

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…

Systems and Control · Electrical Eng. & Systems 2026-03-27 Sebastian Hirt , Lukas Theiner , Maik Pfefferkorn , Rolf Findeisen