Tag: Uncertainty Quantification

• A very, very simple method to estimate Pi

  

  Date: 2026-03-15 Author: Michael T.M. Emmerich Every year, on March 14, mathematicians celebrate Pi Day. For my Mathematical Playground blog, I wished to post a short essay on a very, very simple Monte Carlo method for estimating . The nice aspect of this method is that it requires only a few lines of code, does…

  Michael Emmerich

  March 15, 2026

  Mathematical Playground, Scientific Visualization, Small Python Math Examples

  machine-learning, mathematics, pi, probability, Uncertainty Quantification

• Interval Filters for Pre-Selection in Model-Assisted Constrained Pareto Optimization

  Michael Emmerich, JYU, Finland, 28.1.2026 When objective and constraint evaluations are expensive (CFD/FEM, digital-twin simulations, etc.), we often rely on Gaussian process regression (Kriging) as a surrogate. A GP does not only predict a mean vector, it also delivers uncertainty. Interpreted component-wise, this uncertainty naturally forms an axis-aligned confidence box in for objectives (and similarly…

  Michael Emmerich

  January 29, 2026

  Multicriteria Decision Analysis, Multiobjective Optimization

  Gaussian Process Regression, Kriging, Multiobjective Optimization, Probability Theory, Uncertainty Quantification