All Models Are Uncertain

“All Models Are Uncertain: Case Studies with a Python Grammar of Model Analysis”

A work-in-progress textbook by Zachary del Rosario and Gianluca Iaccarino, to be published by Cambridge Scholar Press.

If you would like to cite this work, please use the following reference:

del Rosario, Z. and Iaccarino, G. (Forthcoming). All Models are Uncertain: Case Studies with a Python Grammar of Model Analysis. Cambridge Scholar Press.

Or use the following bibtex entry:

  title={All Models are Uncertain: Case Studies with a Python Grammar of Model Analysis},
  author={{del Rosario}, Zachary and Iaccarino, Gianluca},
  publisher={Cambridge Scholar Press}


As scientists and engineers we use physical models to solve problems. Leveraging fundamental principles, we can link controllable variables to desired outcomes in applications like designing safe aircraft structures, renewable energy systems, and nuclear waste disposal facilities. However, in all of these systems there are unavoidable sources of uncertainty: manufacturing variation, fluctuating environmental conditions, and a lack of comprehensive physical principles.

A traditional approach to these uncertainties is to throw up one’s hands, pretend uncertainty does not exist, and slap a safety factor on the analysis. This book is about treating uncertainty with the same level of rigor with which we treat physics. Modern techniques in uncertainty quantification (UQ) enable the modeling and assessment of noise and variability. With UQ tools, you can minimize failure rates, distinguish between important and irrelevant uncertainties, and overcome missing physics.

This book is a collection of reproducible case studies on applying UQ to solve science and engineering problems. You will learn to apply advanced UQ techniques in a meaningful context using a Python software package for model analysis under uncertainty—Grama. Learning this computational toolkit will allow you to easily adapt and extend these techniques to your own problems, equipping you to model and predict with confidence.