Quantifying Uncertainties in Engineering Applications


Uncertainty Quantification (UQ) is a set of Machine Learning (ML) methods that puts error bands on results by incorporating real world variability and probabilistic behavior into engineering and systems analysis. UQ answers the question: what is likely to happen when the system is subjected to uncertain and variable inputs. Answering this question facilitates significant risk reduction, robust design, and greater confidence in engineering decisions. Modern UQ techniques use powerful predictive models to map the input-output relationships of the system, significantly reducing the number of simulations or tests required to get statistically defensible answers.

However, applying ML to engineering problems poses several major challenges. For example, many engineering simulations are deterministic, but the underlying problems they model are subject to uncertainties and, therefore, are stochastic in nature. Although ML may produce an optimal solution, it could be one that corresponds to an unrealistic scenario rather than the desired solution incorporating real-world uncertainty. To achieve its true aim, the ML model must be trained in the stochastic nature of the outcomes of interest by incorporating uncertainty into its decision rules. Other challenges include how to understand uncertainties in ML models themselves and how to build such models for sparse or small data sets or data sets with many inputs.

This course will provide an introduction to ML, with particular focus on those tools and techniques required for UQ. There are no prerequisites, and a refresher of required statistics basics will be included. Challenges and solutions to the application of ML to engineering problems will be addressed. Points will be illustrated with examples utilizing SmartUQ software (e.g. NACA airfoil CFD simulation data).

Learning Objectives:

  • Understand the basics of uncertainty
  • Understand the basics of machine learning and UQ techniques
  • How to apply machine learning powered UQ methods to engineering data sets (simulation, digital twin, model-based engineering, experimental, sensor, etc.)
  • Challenges and solutions to machine learning powered UQ for engineering applications
  • How to develop a robust and reliable design with learning powered UQ techniques
  • How to interpret learning powered UQ results when making decisions
Who Should Attend: The attendees for this webinar would be engineers, program managers, and data scientists who want to further investigate how Uncertainty Quantification and Machine Learning can maximize insight, improve design robustness, and increase time and resource efficiency.

Course Length: 1 or 2 days
Course Outline
  • Statistics basics
    • Discrete versus continuous variables
    • Random variables
    • Mean, variance, standard deviation.
    • Histograms, PDFs, CDFs
    • Confidence intervals
  • Supervised Versus unsupervised learning.
  • Forward Prediction Techniques
    • Linear Regression
    • Gaussian Process Models
    • Neural Networks and Deep Learning
  • Assessing ML Model Prediction Accuracy
    • Independent Validation Sets
    • K-fold validation
    • Leave-one-out cross validation
  • Data generation challenges and solutions
    • Design of Experiments (DOEs)
    • Adaptive DOE methods
    • Data sampling
  • Backwards Prediction
    • Inverse Analysis
    • Statistical Calibration
  • Engineering applications of machine learning
    • Acceleration of Simulation efforts
    • Reduction of testing requirements
    • Decision Making Under Uncertainty
    • Virtual Sensors
    • Digital twins
  • Techniques for addressing uncertainty using machine learning models
    • Sensitivity analysis
    • Stochastic Optimization
    • Uncertainty Propagation
Gavin Jones, Principal Application Engineer at SmartUQ, is responsible for performing simulation and statistical work for clients in aerospace, defense, automotive, gas turbine, and other industries. He is a contributor to SmartUQ’s Digital Thread/Digital Twin initiative.


AIAA Training Links