VVUQ · Module 1 of 10

The VVUQ Framework and Model Credibility

Three questions decide whether a simulation can be trusted: are the equations solved right, does the model match reality, and how big is the uncertainty. Verification, validation, and UQ answer them in that order.

Readiness check

This module opens the course. Tick only what you can do closed-notes.

Compute a relative error between two numbers.
Recall that a simulation approximates a mathematical model of reality.
Distinguish a coding error from a modeling assumption.
Recall that measurements carry uncertainty.
State what decision a model is meant to support.

0 or 1 weak itemsContinue with this module.

2 weak itemsRevisit error basics in Numerical Methods, Module 1.

3 or more weak itemsReview the verify-against-theory habit in Finite Element Methods, Module 10.

The core idea

Verification asks whether the equations are solved correctly; validation asks whether the right equations were chosen; uncertainty quantification asks how much the answer could be off. The gap between simulation and reality mixes all three, so they must be separated.

verification: solving the equations rightvalidation: solving the right equationscomparison error E = S − D

A computational result is a prediction that must earn trust before it carries a decision. The ASME VVUQ framework separates the ways it can be wrong. Verification is a mathematics question: does the code solve the chosen equations correctly (code verification), and is the particular solution converged enough (solution verification). Validation is a physics question: do those equations represent reality, judged by comparing the simulation S to experimental data D. Uncertainty quantification asks how much S and D could vary given imperfect inputs, models, and measurements. The observed comparison error E = S − D is not pure model error: it blends numerical error from verification, input uncertainty, and experimental uncertainty. That is why the order matters. You verify first, so that a validation disagreement is not blamed on the physics when it is really a coarse mesh. Credibility, in the ASME V&V 40 sense, is then the accumulated evidence that the model is adequate for its intended use, matched to the consequence of the decision it supports.

The skill works when: you name which of verification, validation, or UQ a question belongs to before answering it.

The skill breaks down when: a validation gap is trusted before the solution is verified, so numerical error masquerades as model error.

The concept. Verification compares the simulation to the mathematics; validation compares it to experiment through E = S − D; UQ bounds how far each could stray. The three answer different questions and must be kept apart.

The skills, taught in order

Five skills fix the vocabulary and the process that the rest of the course builds on.

1.1 Verification

Verification is purely mathematical: it checks that the equations are solved correctly, with no reference to reality. Code verification confirms the software has no algorithm or coding errors; solution verification estimates the numerical error of the specific run. Verification comes first, always.

1.2 Validation

Validation checks that the equations represent the real world, by comparing the simulation to experimental data over the intended range of use. It can only be as good as the data and the verification behind it; a validation claim on an unverified solution is meaningless.

1.3 Uncertainty quantification

UQ characterises how variations in inputs, models, and measurements affect the result. It turns a single number into a number with an interval, which is what a decision actually needs. Verification and validation errors are among the uncertainties it accounts for.

Activity	Question	Compared against
Verification	solving the equations right?	the mathematics
Validation	solving the right equations?	experimental data
Uncertainty quantification	how far could it be off?	input and model variation

The three VVUQ activities and the distinct question each answers. Confusing them is the most common mistake in the field.

1.4 The comparison error

The comparison error E = S − D is the raw disagreement between simulation and experiment. It is a mix of numerical error, model-form error, input uncertainty, and experimental uncertainty. Decomposing E into these parts, rather than blaming the model, is the analytical heart of validation.

1.5 Model credibility and intended use

Credibility is the body of VVUQ evidence that a model is adequate for a specific intended use. The ASME V&V 40 approach scales the required rigor to the model's influence on a decision and the consequence of that decision being wrong: high-stakes uses demand more evidence.

Engineering connection: a stress or flow simulation cannot support a certification decision until it carries verification, validation, and uncertainty evidence proportional to what failure would cost.

Worked example 1: the comparison error

A simulation predicts a peak stress of S = 1.05 (normalised), while a validation experiment measures D = 1.00. Find the comparison error and the relative disagreement.

Figure 1. The comparison error is the raw gap between the simulation and the experiment. It is where validation starts, but not where it ends: the gap must still be decomposed.

ProblemFind the comparison error and relative disagreement in Figure 1.
Given / findS = 1.05, D = 1.00. Find E and the relative error.
AssumptionsThe solution is verified, so E is a meaningful physics comparison, not a mesh artefact.
ModelE = S − D; relative error = E/D.
EquationsE = S − Drelative = E/D
SolveE = 1.05 − 1.00 = 0.05. Relative = 0.05/1.00 = 5%.
CheckThe 5% gap is the total disagreement; whether it signals a real model error depends on the experimental and numerical uncertainties, examined in later modules.
ConclusionThe simulation is 5% above the experiment. That number opens the validation question but does not settle it, because the gap has several sources.

Result. E = 0.05, a 5% comparison error.

Worked example 2: decomposing the gap

For that 5% comparison error (E = 0.05), a grid convergence study shows the numerical error contributes δ_num = 0.012. Estimate the model-form error and its share of the gap.

Figure 2. The comparison error splits into a numerical part, removable by refining the mesh, and a model-form part, the genuine physics discrepancy. Here the model dominates the gap.

ProblemEstimate the model-form error and its share of the gap in Figure 2.
Given / findE = 0.05, δ_num = 0.012. Find δ_model and its fraction of E.
AssumptionsThe gap is dominated by numerical and model-form error, with input and data uncertainty small here.
ModelTreat E as the sum δ_num + δ_model, so δ_model = E − δ_num.
EquationsE = δ_num + δ_modelδ_model = E − δ_num
Solveδ_model = 0.05 − 0.012 = 0.038, which is 0.038/0.05 = 76% of the gap.
CheckRefining the mesh would remove only the 0.012 numerical part, leaving 0.038 of genuine model error; the disagreement is mostly physics, not discretization.
ConclusionAbout three-quarters of the gap is model-form error. Verifying first revealed that refining the mesh cannot close it, so the model itself must be revisited.

Result. δ_model ≈ 0.038, about 76% of the comparison error.

Misconceptions and diagnostics

Mistake	Symptom	Diagnostic question	Correction
Confusing verification and validation	Comparing to data to check the math	"Am I checking the equations or the physics?"	Verification uses mathematics; validation uses experiments.
Validating an unverified solution	Blaming physics for a mesh error	"Is the solution converged?"	Verify first, then validate.
Reporting a bare number	A prediction with no interval	"What is the uncertainty?"	Attach a quantified uncertainty to every result.
Ignoring intended use	Same rigor for every model	"What decision does this support?"	Scale credibility to the consequence.

Practice ladder

Level 1 · Direct skill

A model predicts 240 N and the test measures 250 N. Find the comparison error and relative error.

Show answer

E = 240 − 250 = −10 N; relative = −10/250 = −4%.

Level 2 · Mixed concept

Classify each as verification, validation, or UQ: (a) refining the mesh, (b) comparing to a wind-tunnel test, (c) sampling uncertain material properties.

Show answer

(a) verification (solution), (b) validation, (c) uncertainty quantification.

Level 3 · Independent problem

A 6% comparison error has a numerical part of 0.01 (relative). What is the model-form share?

Show answer

δ_model = 0.06 − 0.01 = 0.05, which is 0.05/0.06 = 83% of the gap. Mesh refinement removes only one-sixth of the disagreement.

Transfer task | Real engineering

For a simulation that will support a safety certification, outline the verification, validation, and UQ evidence you would need before trusting it.

What good work looks like

Code and solution verification (order of accuracy, a grid study), validation against relevant experiments with quantified data uncertainty, and propagated input and model uncertainty, with the rigor scaled to the certification consequence per the credibility framework.

Working with AI, and proving it yourself

Use AI as an examiner, not a solver

"Check that I classified each activity as verification, validation, or UQ correctly."

"Give me three model gaps; I will decompose each into numerical and model parts."

"Is my model valid?" Assembling the evidence yourself is the skill.

"How accurate is this simulation?" Separating the error sources is the point.

Portfolio task

Take a simulation you have run, state the decision it supports, and lay out the verification, validation, and UQ evidence it currently has and lacks.

Must include: a stated intended use, a comparison error, and a verification-versus-validation split of the evidence.

Retrieval and spaced review

Closed notes. Answer out loud, then reveal.

1. What does verification check?

That the equations are solved correctly, a purely mathematical question.

2. What does validation check?

That the equations represent reality, by comparison with experiment.

3. Why verify before validating?

So a validation gap is not blamed on the physics when it is numerical error.

4. Write the comparison error.

E = S − D, simulation minus experimental data.

5. What sets the required credibility?

The model's influence on a decision and the consequence of being wrong.

TodayFinish this quiz and Levels 1 and 2 of the ladder.

+1 dayRe-derive the gap decomposition from a blank page.

+3 daysClassify three new activities as V, V, or UQ.

+7 daysBegin verification in earnest, Module 2.

+30 daysReuse the VVUQ split when reviewing any simulation.

Standards mapping

This module follows the ASME Verification, Validation, and Uncertainty Quantification standards. Use these references to read further.

Topic in this module	Where to read more
The V&V framework and terminology	ASME V&V 10, Computational Solid Mechanics
Comparison error and validation	ASME V&V 20, CFD and Heat Transfer
Credibility and intended use	ASME V&V 40, Model Credibility

Standard designations refer to the ASME V&V series. The framework is also developed in Oberkampf and Roy, Verification and Validation in Scientific Computing.