Bayesian calibration of complex models: theory and practical implementation

Christina Schenk and Ignacio Romero

IMDEA Materials Institute (Spain); Universidad Politecnica de Madrid (Spain)

Relevance to WCCM–ECCOMAS

This short course will discuss topics that have relations with multidisciplinary areas in Applied Computational Mathematics, Data Science, and Mechanics.

Course description

Computational Mechanics relies on models, and all models depend on parameters that must be carefully selected. The goal of this short course is to introduce researchers to the most recent and advanced techniques for model calibration. While the general calibration problem will be outlined, the course will focus on Bayesian methods, which enable a full characterization of the probability distribution of unknown parameters given experimental data and, when available, prior knowledge.

In contrast to traditional point estimation approaches, Bayesian calibration, and in particular the so-called Kennedy and O’Hagan approach, provides a systematic framework to quantify parameter uncertainty and propagate it to model predictions. The course will therefore motivate the need for moving beyond point estimates toward uncertainty-aware calibration, highlighting its importance for robust predictions and informed decision-making. It will also summarize the theoretical foundations underlying these techniques.

Finally, participants will learn how to use ACBICI (A Configurable BayesIan Calibration and Inference Package, an open-source Python package recently implemented by the organizers. This tool simplifies model calibration, providing both a template for novice users and an extensible, object-oriented framework for more advanced applications.

Objectives and target groups

The course is intended for researchers working at the interface between model development and practical applications.

  • Introduce researchers to the most recent and advanced techniques for model calibration.
  • Focus on Bayesian methods.
  • Enable a full characterization of the probability distribution of unknown parameters given experimental data and, when available, prior knowledge.
  • Motivate the need for moving beyond point estimates toward uncertainty-aware calibration.
  • Learn how to use ACBICI (A Configurable BayesIan Calibration and Inference Package).

In this context, full knowledge about model parameters and their uncertainty will prove extremely useful.

Scientific and technical areas covered

  • Computational engineering
  • Mathematical modeling
  • Model calibration (point estimation vs. Bayesian inference)
  • Computational modeling and simulation
  • Optimization and inverse problems
  • Sampling methods (e.g. MCMC)
  • Uncertainty quantification (UQ)

Bio-sketch

Dr. Christina Schenk is a Staff Scientist, Ramón y Cajal Fellow, and head of the ML4Materials Lab at IMDEA Materials Institute, Spain. She holds a Ph.D. in Mathematics from Trier University, Germany, and has over eight years of international research experience in mathematical modelling, simulation, uncertainty quantification, optimisation, Bayesian inference, and data-driven scientific computing across academia and industry. Her research focuses on Bayesian calibration, machine learning, and computational methods for complex physical and engineering models, with applications spanning materials science, chemical manufacturing, environmental science, healthcare, and food production. She has held research positions at Carnegie Mellon University, the Basque Center for Applied Mathematics (BCAM), and Lawrence Berkeley National Laboratory.

Dr. Schenk has authored more than 28 publications, contributed to numerous interdisciplinary research projects, and developed several open-source computational tools for modelling, optimisation, and AI-driven decision-making. Her work bridges mathematical theory and practical implementation, with a strong emphasis on scalable computational methods and real-world applications.

Prof. Ignacio Romero is Full Professor at the Department of Mechanical Engineering at the Technical School of Industrial Engineering (ETSII) in the Technical University of Madrid (UPM) and Senior Researcher of IMDEA Materials Institute, where he leads the Computational Solid Mechanics group. From 2017 to 2021 he was also the director of this public research institute of the Comunidad de Madrid.   He obtained a degree in Industrial Engineering, with a major in Mechanical Engineering, from the ICAI School of the Universidad Pontificia Comillas (Madrid). After one year working as a researcher in the Institute for Technological Research (Madrid), he obtained a M. Sc. in Mechanical Engineering from Stanford University (US), and later a Ph.D. in Civil and Environmental Engineering from the University of California at Berkeley. Previously, he has been a Fulbright Scholar (1997), a post-doctoral researcher at U.C. Berkeley (2001), a Visiting Professor at UPM (2001), a “Ramón y Cajal” researcher, and an Associate Professor also at UPM (2005-2011). He has been a visiting professor at the California Institute of Technology (2011/12) and at the University of British Columbia (2023).  

His research lines are nonlinear dynamics of solids, nonlinear solid and structural mechanics, and multiscale material modelling. His work has been published in international journals of Computational and Applied Mechanics, and he has given invited seminars in universities of Europe and the United States. In 2011, in recognition of his work, he received the Zienkiewicz medal and prize for the best article in the field of Computational Mechanics by a researcher under the age of 40. Having advised 12 PhD students in the past, he is currently advising another five. He has participated in 25 national and international competitive projects and served as PI on 5 projects of the National Spanish Research Program. He has published 80 peer-reviewed journal articles and 5 book chapters.   As part of his technology transfer activities, he is the primary developer of an object-oriented, general-purpose finite element code, IRIS (https://materials.imdea.org/iris/), now a registered software, and MUESLI (https://materials.imdea.org/muesli/), an open-source library for material modelling, and co-developer of ACBICI (https://gitlab.com/schenkch/ACBICI).