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Module 18 · Lesson 18.4

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.

Why 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

What a surrogate is for

A nonlinear analysis takes twenty minutes. You want to explore two hundred parameter combinations. That is nearly three days of computation, which is more than the design programme allows.

So: run forty combinations properly, fit a model to those results, and evaluate the model two hundred times in a second. Then run the promising combinations properly to confirm.

That last sentence is the whole discipline. The surrogate narrows the search; the deterministic analysis confirms the answer. Skip the confirmation and the surrogate has stopped being a search tool and become the analysis.

Inside and outside

The library fits a cubic surrogate to a genuinely nonlinear function over the range 0 to 6, then evaluates it out to 14:

Error
Inside 0 to 6 (interpolation)0.066
Outside 6 to 14 (extrapolation)45.85

That is a factor of about 695.

Inside its data the surrogate is excellent — accurate enough to rank designs reliably and explore with confidence. Outside it, it is a cubic polynomial doing what cubic polynomials do, which is diverge.

Nothing in the output says which

This is the part that matters.

Ask the surrogate for a value at 3 and it returns a number. Ask it at 13 and it returns a number. Both are ordinary floating-point values, formatted identically, delivered with the same speed and the same absence of caveat.

The model has no representation of 'where my data was'. It is a function, defined everywhere.

So the boundary has to be enforced by the engineer, and it has to be enforced explicitly: record the range of every input in the training set, and refuse — or at minimum flag — any query outside it. That is a piece of bookkeeping, not a piece of cleverness, and it is the difference between a useful tool and a confident liar.

The rule

Where a deterministic check exists, it must have been run.

Not 'should ideally'. A recommendation whose deterministic check is available and unrun may not be acted on, whatever the confidence attached to it, because confidence is a property of the model's fit and not evidence about the structure.

The library enforces exactly this: a recommendation with an available-but-unrun check returns allowed: false, with the reason.

What a recommendation must carry

Four things, and none is optional:

Evidence. What the recommendation is based on. Without it there is nothing to review.

Uncertainty. Stated honestly, including that a confidence figure is not a probability of being right.

What would make it wrong. The condition under which the recommendation fails. This is the most useful field and the most often omitted — it is what lets a reviewer check the one thing that matters.

The deterministic check, and whether it has been run.

Then a named human reviews it and records a decision. Not because a process requires it, but because:

The qualified engineer remains accountable for the decision, whatever tool informed it. No tool accepts that accountability, and none can.

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

trained hereinput →true (solid) · surrogate (dashed)
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 a surrogate model's output tell you about whether it is extrapolating?

    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
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    This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint