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Learn · Multi-fidelity optimisation
Your design review trusts the full-fidelity solve, and your programme can afford only a few. TensorLynx lets coarse meshes, simpler physics and surrogates do the searching, learns how they differ from the full model, and spends expensive solves where cheap ones cannot decide. A cheap model joins only when the data show it is related.
Co-kriging with a negative-transfer guardPooling refused by default, with reasonsFinal word: an independent full-model re-run
The cost of the old way
A full-fidelity CFD or FEA run on a production mesh settles design reviews, and a programme can afford a handful. Teams then fall into one of three habits, each of which sends the bill later.
The research view: low-fidelity models give the speed, “while the high-fidelity model is kept in the loop”.
Peherstorfer, Willcox & Gunzburger, survey of multifidelity methods [1]. TensorLynx builds that discipline into the workflow.
How TensorLynx does it
The cheapest rung is often a model you already have: a trust-aware surrogate or a full-field reduced-order model. Six steps turn a ladder of such models into one decision you can defend.
Every rung covers the same design space: a surrogate from earlier runs, a coarse mesh, simpler physics, and the full model your review signs off. Results from another design space are never pooled, since one design vector would mean two shapes. A coarse rung is useful only when you know how coarse it is, which mesh verification establishes.
A few full-model results anchor the truth. They rarely sit on the cheap curve, and that offset is exactly what the method learns.
TensorLynx fits recursive co-kriging: the full model as ρ times the cheap model plus a learned discrepancy δ, each a Gaussian process. Verified gradients join the fit where they exist; a missing gradient is skipped, never filled with zero. The optimiser is served the gradient of the full-model prediction itself.
The scaling ρ is integrated out, not regressed on a handful of points, and the evidence the cheap data buy is measured. Below a declared bar, ρ is zero and the model is exactly the full-only fit. Co-kriging is kept only if, on held-out full-model designs, it helps against full-only training.
The cheap model proposes; the expensive solver disposes. Inside a trust region the model predicts an improvement, the full solver measures it, and their agreement decides whether the step is accepted and how far the next one may go, the classic pattern of variable-fidelity model management [5]. A point where the solver did not converge never becomes the new centre.
The recommended design is the best evaluated, feasible, converged design on solver values, never on predictions. It is verified only by an independent re-run (see high-fidelity reassessment), and choosing it stays an engineer's decision.
Schematic Curves and counts are illustrative; the mechanism, the gate and the labels are the platform's.
Inside the engine
yf(x) = ρ·yc(x) + δ(x)
gain = ln L(with ρ·μc) − ln L(full only) ≥ 3 nats
Evidence you can check
Each item names its evidence type. What you get is not a headline saving, which depends on how well your rungs agree, but refusals and decisions you can read back.
Both live in the platform's AI/ML layer, with automated tests that pin each behaviour: an unrelated cheap model earns next to no evidence, so the result is exactly the full-only fit; four full-model designs cannot establish a relation; too few designs and mismatched inputs are refused; a missing gradient is skipped, never zero-filled.
A recorded verification run pools 30 cheap designs into 8 or 15 expensive ones, over 20 replicates, for three synthetic stand-ins for different discretisations of one intake-duct physics, with the data-generating process in the record. Four negative controls must be refused. The refusal verdict: PASS.
On a recorded pipe-bend run, a surrogate proposed and the discrete adjoint CFD solver measured. The loop took a null step without calling the solver when the model saw no gain, accepted a step the solver confirmed, and refused to move its centre to a point where the solver had not converged. The delivered design was then verified with fresh primal and adjoint solves on its own mesh.
The recommendation is the best evaluated feasible design on solver values; “verified” is granted only by an independent re-run, never by an optimiser's exit.
What it changes for your programme
Cheap rungs map the trend, the full model decides, and a misleading cheap model is left out, with the reason on record.
One ladder, one model, one guard. Gradients belong to the full-model prediction, and every refusal is stated in words you can put in a report.
The plan states how many evaluations a run makes and how sure that count is, and shows a cost only where one has been measured.
On an engagement we build the ladder around your product, check each rung's design space, run the transfer test before pooling, and leave the final word to the full model. The MDAO chapter then carries the decision across disciplines and constraints.
Intakes and wing sections: coarse and simpler-flow rungs explore; production-mesh RANS is kept for candidates near the decision.
Blade and passage families: an earlier campaign becomes a rung, provided the design space matches and its data may be reused.
Heat exchangers, manifolds, cold plates: a coarse conjugate heat-transfer model maps trends; the full model confirms the shortlist.
Cooling ducts and underhood flows: last programme's surrogate is the cheapest rung, and the guard decides whether it still fits the new geometry.
| Question | Typical workflow | With TensorLynx |
|---|---|---|
| Cheap results | Best design taken from the coarse model, checked late | Cheap rungs map the trend; the full model anchors and decides |
| Correction | A factor fitted by hand to a few points | Co-kriging: ρ integrated out, the discrepancy learned |
| A misleading cheap model | Discovered on the final run | Below 3 nats of evidence it is dropped, and the reason recorded |
| Other data | Copied in if it looks similar | Refused unless same design space, reuse permitted, enough designs and a passed held-out test |
| Budget | Counted afterwards | Evaluation count and its certainty shown before the run |
| Final answer | Best predicted design | Best evaluated feasible design, verified only by an independent re-run |
FAQ
Design optimisation that combines many cheap evaluations, such as coarse-mesh runs, simpler physics or surrogates, with a few full-fidelity solves. Cheap models explore, a learned correction links them to the full model, and the full model confirms the answer.
It depends on how closely your cheap rungs track the full model, so we quote no generic figure. TensorLynx tests the relation per case, against full-model-only training on held-out designs, and keeps a cheap rung only when it helps.
A coarser mesh, simpler physics, a surrogate or reduced-order model trained on earlier runs, or results from another solver or campaign. Each must cover the same design space as the full model, and data you are not entitled to reuse is refused.
The cheap data must buy at least 3 nats of evidence before the scaling between fidelities may differ from zero. Below that bar the model is exactly the fit to full-model data alone, and the record states that the cheap rung was not used and why.
No. The recommended design is the best evaluated, feasible, converged design on solver values, and it is labelled verified only after an independent re-run. Predictions steer the search; the full model decides, and an engineer makes the choice.
We start from your full model and the cheaper models you already trust, check their design spaces and run the transfer test before pooling. Full-model solves go where cheap rungs cannot decide, and you receive the decision with every refusal and verification on record.
Back to the TensorLynx overview.
Every capability hands its result to the next on the same model, the same units and the same record: geometry feeds physics, physics feeds sensitivities and learning, optimisation proposes, verification confirms, and the history keeps every step reproducible.
TensorLynx is built and run by the engineers who use it on client work. You can start small, with one geometry and one question, and grow into a workflow your own team owns.
Send a geometry, the objective and the constraints. We tell you which TensorLynx route answers it, what it needs from you, and what you will get back.
Our engineers run the loop on your problem: physics, sensitivities, optimisation and full-model verification, handed over with every setting on record.
A TensorLynx workflow, surrogate and verification gates set up around your product family, so the next design cycle starts where the last one ended.
Your team on TensorLynx, trained on your own cases, with OLTRION engineers behind it for the questions that need a specialist.
Simulation and AI predictions support engineering decisions; they do not replace the testing, approval and sign-off a product requires. Figures marked measured come from recorded TensorLynx runs on the stated case; figures marked synthetic or schematic illustrate a method.
