Chapter 4 -- When a surrogate is faithful enough (RQ2)¶
Why the question arises here¶
brief: Two paragraphs. Connect to chapter 3's result -- the full-order model missed its deadline on 40% of the operating envelope -- and say what RQ2 asks. No literature dump; the examiner has just read three chapters and wants the thread, not a re-introduction.
What "faithful enough" has meant¶
claim: Fidelity in this literature is defined against a decision rather than in the abstract, but the field has no shared threshold, so published fidelity claims are not comparable across papers.
brief: This section carries the chapter's terminology load. Every term in the glossary should be used in its pinned sense at least once here, because the examiner reads later sections against this one.
queries:
- surrogate model fidelity criterion
- reduced order model validation
- model accuracy requirement safety critical
Methods that bound the error¶
brief: The technical core. Prefer a source that states a bound over one that reports an empirical fit -- and where a paper reports a fit and calls it a bound, say so rather than repeating its claim.
queries:
- reduced order model error bound
- a posteriori error estimator projection
- surrogate uncertainty quantification
Projection-based bounds¶
brief: The family this thesis extends. Deepest treatment in the chapter.
queries:
- proper orthogonal decomposition error bound
- greedy reduced basis a posteriori
Bounds that assume linearity¶
claim: The available a-priori bounds assume a linearity that the water-network model of chapter 5 does not satisfy anywhere near its operating point.
queries:
- error bound linear assumption violated
- nonlinear model order reduction guarantee
Why the existing bounds do not transfer¶
brief: The gap that motivates chapter 5, argued rather than asserted. Be explicit that the argument is mine and mark exactly which step the corpus supports and which it does not -- an examiner will find the seam anyway, and finding it flagged reads as rigour.
queries:
- error bound assumptions violated nonlinear
- reduced model extrapolation operating envelope
What this chapter establishes¶
brief: Half a page. State what RQ2 is now answered with, and hand over to chapter 5. No new citations.