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Verification, Validation and Uncertainty Quantification in Scientific Computing

O​nline Training Course

Verification, Validation and Uncertainty Quantification in Scientific Computing

2​1 - 24 October 2024 | Online (Webex)

Engineering systems must increasingly rely on computational simulation for predicted performance, reliability, and safety. Computational analysts, designers, decision makers, and project managers who rely on simulation must have practical techniques and methods for assessing simulation credibility. This short course presents modern terminology and effective procedures for verification of numerical simulations, validation of mathematical models, and uncertainty quantification of nondeterministic simulations.

The techniques presented in this course are applicable to a wide range of engineering and science applications, including fluid dynamics, heat transfer, solid mechanics, and structural dynamics. The mathematical models considered are given in terms of partial differential or integral equations, formulated as initial and boundary value problems. The computer codes that implement the mathematical models can use any type of numerical method (e.g., finite volume, finite element) and can be developed by commercial, corporate, government, or research organizations. A framework is provided for incorporating a wide range error and uncertainty sources identified during the modeling, verification, and validation processes with the goal of estimating the total prediction uncertainty of the simulation.

While the focus of the course is on modeling and simulation, experimentalists will benefit from a detailed discussion of techniques for designing and conducting high quality validation experiments. Application examples are primarily taken from the fields of fluid dynamics and heat transfer, but the techniques and procedures apply to all application areas in engineering and science. The course closely follows the course instructors’ book, Verification and Validation in Scientific Computing, Cambridge University Press (2010).

Who Should Attend?

Model developers, computational analysts, code developers, software engineers, and experimentalists working with computational analysts. Managers directing simulation work and project engineers relying on computational simulations for decision-making will also find this course beneficial.

Upon completion of this course, attendees will be able to:

  • Define the objectives of verification, validation, and uncertainty quantification
  • Implement procedures for code verification and software quality assurance
  • Implement procedures for solution verification, i.e., numerical error estimation
  • Plan and design validation experiments
  • Understand procedures for model accuracy assessment
  • Comprehend the concepts and procedures for non-deterministic simulation
  • Identify sources of uncertainty, such as aleatory and epistemic uncertainties
  • Recognize the goals of model parameter calibration/updating
  • Interpret local and global sensitivity analyses
  • Recognize the practical difficulties in implementing VVUQ technologies

Course Materials Provided

Course attendees will be provided with a copy of the book Verification and Validation in Scientific Computing, Cambridge University Press (2010). Registrants outside of the United States will receive an e-book version. The 780-page book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification, validation, and uncertainty quantification for models and simulations. The book contains several examples of the most common procedures in VVUQ, including an example of the design and execution of a high quality validation experiment. Once the course materials have shipped, the course fees are nonrefundable.

Course Program

The contents are presented in eight sessions, two per day, tentatively organized as shown. The schedule allows for ample discussion and interaction with the instructors and other attendees. The instructors reserve the right to modify the contents to address the audience’s needs and preferences.

Session 1. Introduction, Background, and Motivation
Session 2. Terminology and Fundamental Concepts
  • Brief history of terminology
  • Present definitions and interpretations
  • Alternate definitions used by related communities
  • Additional important terms
  • Who should conduct verification, validation, and uncertainty quantification?
Session 3: Code Verification
  • Software engineering
  • Criteria and definitions–Order of accuracy
  • Traditional exact solutions
  • Method of manufactured solutions
Session 4: Solution Verification
  • Round-off error
  • Iterative convergence
  • Iterative error estimation
  • Discretization error estimation
  • Reliability of discretization error estimators
  • Discretization error and uncertainty estimation
  • Solution adaptation procedures
Session 5: Validation Experiments
  • Validation fundamentals
  • Validation experiment hierarchy
  • Validation experiments vs. traditional experiments
  • Six characteristics of validation experiments
  • Detailed example of a wind tunnel validation experiment
Session 6: Model Accuracy Assessment
  • What are validation metrics?
  • Various approaches to validation metrics
  • Recommended characteristics for validation metrics
  • Identification of model discrepancy
  • Cumulative distribution function approach
Session 7: Predictive Capability of Modeling and Simulation
  • Identify all sources of uncertainty
  • Characterize each source of uncertainty
  • Estimate solution error in system responses of interest
  • Estimate total uncertainty in system responses of interest
  • Procedures for updating model parameters
  • Types of sensitivity analysis
Session 8: Final Topics
  • Planning and prioritization in modeling and simulation
  • Maturity assessment of modeling and simulation
  • Practical difficulties in implementing VVUQ technologies


PSE Competencies addressed by this training course

V&V-SIMMsy9Design a test for analysis validation purposes.
V&V-SIMMsy8Formulate a series of smaller studies, benchmarks or experimental tests in support of a simulation modelling strategy.
V&V-SIMMsy7Prepare a validation plan in support of a FEA study.
V&V-SIMMkn6State simulation V&V principles
V&V-SIMMkn15List relevant physical tests and their characteristics to calibrate or validate simuation.
V&V-SIMMev8Train engineering staff in validation techniques
V&V-SIMMev7Design appropriate verification and validation procedures in support of simulation.
V&V-SIMMev11Design test/analysis correlation processes, and select analysis validation criteria.
V&V-SIMMev10Assess model/analysis validity from test/analysis correlation studies
V&V-SIMMco9Explain the term model calibration.
V&V-SIMMco8Explain the term code verification.
V&V-SIMMco7Explain the term solution verification.
V&V-SIMMco6Explain the terms Verification and Validation.
V&V-SIMMco32Understand simulation error assessment methodologies and the concept of simulation predictive maturity.
V&V-SIMMap6Perform test /analysis correlation studies
V&V-SIMMap5Perform model calibration from tests
V&V-SIMMap4Perform basic model checks
V&V-SIMMap3Conduct validation studies in support of simulation.
V&V-SIMMan7Analyze test data to support validation activities
V&V-SIMMan6Analyze simulation results to support validation activities.
PROBkn8List types of uncertainty
PROBkn5List typical random sampling techniques.
PROBkn3List the characteristics of a typical probability distribution
PROBkn10List the benefits from probabilistic finite element analysis.
PROBkn1List typical sources of uncertainty in a reliability assessment
PROBco9Explain the relationship between the Normal Probability Density Function and the Cumulative Density Function.
PROBco8Explain how probabilistic sensitivities can be used to guide product design.
PROBco7Describe how variability in an analysis input quantity may be characterised.
PROBco2Describe the difference between epistemic and aleatoric uncertainty and how they can be quantified
PROBco11Describe Monte Carlo simulation.
PROBco1Explain the term non-deterministic.
MG-SIMMsy15Implement efficient versioning process for the simulation tools used by your company.
MG-SIMMev9Evaluate and benchmark external supplier validation approach
MG-SIMMev14Assess simulation solution maturity and readiness levels for a new project.
MG-SIMMco33Understand software versioning processes
MG-SIMMco1Understand the need and relevance of analysis specifications.
MG-SIMMap25Apply appropriate procedures for controlling the quality of simulation work
MG-SIMMap18Monitor tool (code) verification for the relevant project and intended use
MESMev1Select appropriate validation measures.
MESMco9Discuss the uncertainties typically present in analyses and explain how these are handled.
FEAsy8Prepare a validation plan in support of a FEA study.
FEAkn4Define the meaning of adaptive mesh refinement
FEAkn13State the word length or arithmetic precision of calculations for any system used.
FEAev5Manage verification and validation procedures in support of FEA.
FEAco3Explain the term solution residual.
FEAco12Outline a common method employed to solve the large sets of sparse symmetric common in FEA.
CFDsy3Formulate a plan to address the uncertainty in input data or modelling when using a CFD code for a design study.
CFDkn7List the main sources of error and uncertainty that may occur in a CFD calculation.
CFDco12Review the issues associated with the estimation of total uncertainty in a flow simulation.


Event Type Training Course
Member Price £1184.48 | $1525.00 | €1405.41
Non-member Price £1495.16 | $1925.00 | €1774.04
Tutor: Christopher Roy
Tutor: William Oberkampf


Start Date End Date Location

Session Times


Course Information

Course Start and End Times:
Two 2-hour sessions / day

07:00 - 12:00 (Los Angeles) | 10:00 - 15:00 (New York)
1​5:00 - 20:00 (London) | 16:00 - 21:00 (Berlin)
(This includes two short coffee breaks and lunch break)

In-house Course

This course can be booked as in-house course. Please request a quote.

Cancellation Policy

  • Up to 6 weeks before course starts: free of charge;
  • Up to one week before: 75 %;
  • Later and no show: 100 %.
Course Cancellation
If not enough participants we keep the right to cancel the course one week before. The course can be cancelled also in case of force majeure. In these cases the course fees will be returned.


Accreditation Policy

The course is agreed and under control of NAFEMS Education and Training Working Group.


Still Curious?

Discover the valuable insights and knowledge waiting for you in our course by joining our captivating taster webinar today.