@inproceedings{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins}, series = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, booktitle = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, pages = {1 -- 15}, abstract = {In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat-FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {A Bayesian Framework for Simulation-based Digital Twins of Bridges}, series = {EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability}, volume = {6}, journal = {EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability}, number = {5}, doi = {10.1002/cepa.2177}, pages = {734 -- 740}, abstract = {Simulation-based digital twins have emerged as a powerful tool for evaluating the mechanical response of bridges. As virtual representations of physical systems, digital twins can provide a wealth of information that complements traditional inspection and monitoring data. By incorporating virtual sensors and predictive maintenance strategies, they have the potential to improve our understanding of the behavior and performance of bridges over time. However, as bridges age and undergo regular loading and extreme events, their structural characteristics change, often differing from the predictions of their initial design. Digital twins must be continuously adapted to reflect these changes. In this article, we present a Bayesian framework for updating simulation-based digital twins in the context of bridges. Our approach integrates information from measurements to account for inaccuracies in the simulation model and quantify uncertainties. Through its implementation and assessment, this work demonstrates the potential for digital twins to provide a reliable and up-to-date representation of bridge behavior, helping to inform decision-making for maintenance and management.}, language = {en} } @inproceedings{VillaniUngerWeiser, author = {Villani, Paolo and Unger, J{\"o}rg F. and Weiser, Martin}, title = {Adaptive Gaussian Process Regression for Bayesian inverse problems}, series = {ALGORITMY 2024 Proceedings}, booktitle = {ALGORITMY 2024 Proceedings}, abstract = {We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems.}, language = {en} } @inproceedings{GhannamMexiLametal., author = {Ghannam, Mohammed and Mexi, Gioni and Lam, Edward and Gleixner, Ambros}, title = {Branch and price for the length-constrained cycle partition problem}, series = {Proceedings of INFORMS Optimization Society Conference}, booktitle = {Proceedings of INFORMS Optimization Society Conference}, language = {en} } @article{BolusaniBesanconGleixneretal., author = {Bolusani, Suresh and Besan{\c{c}}on, Mathieu and Gleixner, Ambros and Berthold, Timo and D'Ambrosio, Claudia and Mu{\~n}oz, Gonzalo and Paat, Joseph and Thomopulos, Dimitri}, title = {The MIP workshop 2023 computational competition on reoptimization}, series = {Mathematical Programming Computation}, volume = {16}, journal = {Mathematical Programming Computation}, doi = {10.1007/s12532-024-00256-w}, pages = {255 -- 266}, abstract = {This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge was to accelerate the proof of optimality of the modified instances by leveraging the information from the solving processes of previously solved instances, all while creating high-quality primal solutions. Specifically, we discuss the competition's format, the creation of public and hidden datasets, and the evaluation criteria. Our goal is to establish a methodology for the generation of benchmark instances and an evaluation framework, along with benchmark datasets, to foster future research on reoptimization of mixed integer linear optimization problems.}, language = {en} } @article{CardereraBesanconPokutta, author = {Carderera, Alejandro and Besan{\c{c}}on, Mathieu and Pokutta, Sebastian}, title = {Scalable Frank-Wolfe on generalized self-concordant functions via simple steps}, series = {SIAM Journal on Optimization}, volume = {34}, journal = {SIAM Journal on Optimization}, number = {3}, doi = {10.1137/23M1616789}, language = {en} } @inproceedings{EiflerWitzigGleixner, author = {Eifler, Leon and Witzig, Jakob and Gleixner, Ambros}, title = {Branch and cut for partitioning a graph into a cycle of clusters}, series = {Combinatorial Optimization. ISCO 2024}, volume = {14594}, booktitle = {Combinatorial Optimization. ISCO 2024}, doi = {10.1007/978-3-031-60924-4_8}, abstract = {In this paper we study formulations and algorithms for the cycle clustering problem, a partitioning problem over the vertex set of a directed graph with nonnegative arc weights that is used to identify cyclic behavior in simulation data generated from nonreversible Markov state models. Here, in addition to partitioning the vertices into a set of coherent clusters, the resulting clusters must be ordered into a cycle such as to maximize the total net flow in the forward direction of the cycle. We provide a problem-specific binary programming formulation and compare it to a formulation based on the reformulation-linearization technique (RLT). We present theoretical results on the polytope associated with our custom formulation and develop primal heuristics and separation routines for both formulations. In computational experiments on simulation data from biology we find that branch and cut based on the problem-specific formulation outperforms the one based on RLT.}, language = {en} } @article{GuptaHamannMueyesseretal., author = {Gupta, Pranshu and Hamann, Fabian and M{\"u}yesser, Alp and Sgueglia, Amedeo and Parczyk, Olaf}, title = {A general approach to transversal versions of Dirac-type theorems}, series = {Bulletin of the London Mathematical Society}, journal = {Bulletin of the London Mathematical Society}, language = {en} } @article{BarrosCavalarMotaetal., author = {Barros, Gabriel F. and Cavalar, Bruno P. and Mota, Guilherme O. and Parczyk, Olaf}, title = {Anti-Ramsey threshold of cycles for sparse graphs}, series = {Discrete Applied Mathematics}, journal = {Discrete Applied Mathematics}, language = {en} } @article{KohayakawaMotaSchnitzeretal., author = {Kohayakawa, Yoshiharu and Mota, Guilherme O. and Schnitzer, Jakob and Parczyk, Olaf}, title = {Anti-Ramsey threshold of complete graphs for sparse graphs}, series = {Discrete Mathematics}, journal = {Discrete Mathematics}, language = {en} }