Computational Engineering / AI and machine learning for structural engineers
Surrogates, and who is accountable
A fast approximation to a slow analysis — what it buys, what it costs off the edge of its data, and the rule that governs its use.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Checks needed for project use
- A computational engineering reviewer must check algorithms, convergence claims, statistical assumptions and numerical examples beyond the cases explicitly recorded.
- Reproduce seeded learning experiments and label model-selection data as validation, retaining an independent test procedure.
- Obtain qualified review for legal responsibility statements; this is not a legal opinion.
- Review domain guards and calibration before any real engineering use.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
The most genuinely useful application of machine learning in structural engineering is the surrogate: fit a fast approximation to a slow analysis, then explore a design space in seconds that would have taken days.
It is also the application where the failure mode is most dangerous, because the surrogate's output looks identical whether it is interpolating within its data or extrapolating far outside it.
By the end of this lesson you should be able to
- Explain what a surrogate is for and what it replaces
- Quantify the interpolation and extrapolation error and compare them
- Explain why nothing in the output signals extrapolation
- State and apply the deterministic-check rule
- Say what a recommendation must carry to be reviewable
Surrogate role
A surrogate approximates an expensive calculation to help explore candidate designs. Count both the analyses used to fit it and the confirming analyses when assessing the saving. Validate predictions over the intended input domain and confirm selected decisions through the required engineering checks.
In this particular polynomial demonstration, the reported errors are 0.066 inside the fitted interval and 45.85 outside, a ratio of 694.7. That illustrates extrapolation risk; it does not predict the error of a different surrogate, nor prove that every in-range ranking is reliable.
Record the data domain and inspect new inputs. Individual minimum/maximum ranges are useful but do not prove that a multidimensional combination is represented; sparse interior regions and changed physical conditions also matter. Surrogates can include uncertainty or domain checks, but these need validation too.
The teaching workflow requires an available engineering confirmation check before approving a recommendation. Record the evidence, uncertainty, applicability limits, checks and responsible reviewer. Use of a tool does not remove professional responsibilities; any allocation of legal duties between organisations requires appropriate review.
Try it
Surrogate model explorer
Fit a fast approximation to a slow function over one range, then query it outside. The error rises by orders of magnitude and nothing about the output changes.
Underlying function
- Query at
- 13.00
- Inside the trained range?
- no — trained only to 6
- Surrogate says
- 101.1853
- True value
- 26.2105
- Error at this query
- 74.9747
- Interpolation error (RMS)
- 0.0660
- Extrapolation error (RMS)
- 45.85
- Extrapolation penalty
- × 695
The surrogate returned 101.185 in the same format, at the same speed, with no warning. It has no representation of where its data was — it is a function, defined everywhere.
What the engineer has to do
- Record the range of every input in the training set. That is bookkeeping, not cleverness, and it is the only defence.
- Check every query against it, and refuse or flag anything outside.
- Confirm the promising candidates with the deterministic analysis. The surrogate searches; the analysis answers.
- Try the cubic function: when the truth is in the surrogate's own family, extrapolation is nearly free. That is a fact about that function, not a general licence.
What this shows: Nothing in a surrogate's output distinguishes an interpolation from an extrapolation — the boundary has to be enforced by the engineer.
Try it
Human approval workflow
A recommendation with evidence, uncertainty and a deterministic check. Try to get it approved with the check unrun.
Evidence recorded
Deterministic check
Human review
Recommendation
Increase the transfer beam from a 762 UB to an 838 UB
- Confidence
- 94 % — which describes how well the model fits its training data, and is not a probability that this is right.
- Evidence
- Comparable spans in the training set used a deeper section; Deflection is the governing check in 8 of 10 similar cases
- What would make it wrong
- The floor zone cannot accommodate the extra 76 mm of depth
- Deterministic check
- Available and not run.
- May this be acted on?
- no
- Blockers
- 2
Why not
- A deterministic check exists for this and has not been run. Confidence is not evidence where a calculation is available.
- No human review recorded.
Try this
- Set the confidence to 100 % with the check unrun. It still cannot be acted on — confidence is not a substitute for a calculation that could have been done.
- Set the check to 'none exists'. Now confidence and evidence and a review are what you have, which is the situation where a recommendation genuinely helps.
- Remove the evidence. Without it there is nothing for a reviewer to examine, so the review would be a formality.
- Reject at review. A recorded rejection is as useful as an acceptance — it says the question was considered.
What this shows: Where a deterministic check exists it must have been run — confidence is a property of the model's fit, not evidence about the structure.
Worked example
A surrogate used just outside its range
Given
- A surrogate fitted over spans of 6 to 12 m from 40 nonlinear analyses
- Interpolation error within that range: about 0.07 in the objective's units
- The same surrogate queried at a 15 m span, because a late design change extended one bay
Find
What the surrogate returns and what should happen
Practice
A surrogate has an interpolation error of 0.066 and an extrapolation error of 45.85. By what factor is extrapolation worse? Give the factor to the nearest ten.
Practice
A nonlinear analysis takes 20 minutes. A study needs 200 combinations. A surrogate is fitted from 40 real runs and used for the rest, with the best 10 confirmed properly. How many minutes of analysis does that take, against running all 200?
Check yourself
A recommendation carries 94 % confidence, full evidence, a named reviewer who has accepted it — and a deterministic check that exists and has not been run. May it be acted on?
Practice
A surrogate runs in 0.02 seconds against a full analysis at 40 seconds. How many times faster is it?
Practice
Building a surrogate needs 200 full analyses at 40 seconds each. How many minutes of computation is that?
Check yourself
What does the numerical prediction alone reveal about extrapolation in the plain polynomial surrogate used here?
Check yourself
Who is accountable for a design decision made on the strength of an AI recommendation?
Summary
- A surrogate narrows the search; the deterministic analysis confirms the answer
- Interpolation error 0.066, extrapolation error 45.85 — a factor of about 695
- Nothing in the output distinguishes the two, because a fitted function is defined everywhere
- Record the training range and check queries against it — bookkeeping, not cleverness
- Where a deterministic check exists, it must have been run
- A recommendation carries evidence, uncertainty, what would make it wrong, and the check
- The qualified engineer remains accountable, and no tool accepts that accountability