Date: 21 September 2025
Time: 14:00 – 18:00
Location: To be defined

Lecturers:
Knut Andreas Meyer (Chalmers University of Technology)
Henning Wessels (TU Braunschweig)
Hermann G. Matthies (TU Braunschweig)

This short course is comprised of four lectures:

• 14:00 – 14:45: Constitutive modeling enhanced by machine learning
  Knut Andreas Meyer
  The enhancement of traditional constitutive models by machine learning is paving the way for automatically discovering new and better models. This lecture gives an overview of recent approaches in physically constrained machine learning-enhanced constitutive models, while reviewing fundamental theories and discussing examples from the literature.


• 15:00 – 15:45: Inverse problems (deterministic)
  Henning Wessels
  Parameter identification approaches relying on full-field measurement data constitute an inverse problem. Adopting concepts discussed in the inverse problems community, we distinguish between all-at-once (or one-shot) and reduced approaches. With this general framework, we are able to structure a large portion of the literature on parameter estimation in computational mechanics.


• 15:45 – 16:15: Coffee break


• 16:15 – 17:00: Bayesian Assimilation and Updating I
  Hermann G. Matthies
  – Inverse Problems and Bayesian Assimilation or Updating for Identification
  – Probabilistic Modelling of Knowledge, Random Variables and Expectation
  – Vector valued Random Variables and Random Fields, Analysis via Linear Maps
  – Basic Algorithms for Uncertainty Quantification, Monte Carlo and Spectral Methods


• 17:15 – 18:00: Bayesian Assimilation and Updating II
  Hermann G. Matthies
  – Conditional Expectation, Conditional Probability, Different Forms of Bayes's Theorem
  – Probabilistic and Deterministic Algorithms, Markov Chain Monte Carlo Methods
  – The Filtering Idea, Particle Filter, Projections, the Kalman Filter and its Generalisations
  – Reduced Order Models and Machine Learning as Conditional Expectation