AI for Engineering Productivity
AI design optimization with FEA, worked step by step: a 12-point DOE, a Gaussian process surrogate and a bracket optimum found in 13 solver runs.
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5 min read
Dr. Maor Farid
Maor Farid is the Co-Founder and CEO of Leo AI, the first AI platform purpose-built for mechanical engineers. He holds a PhD in Mechanical Engineering and completed postdoctoral research at MIT as a Fulbright fellow. A Forbes 30 Under 30 honoree and former AI researcher and Mechanical Engineer in an elite military intelligence, Maor leads Leo AI's mission to transform how engineering teams design better products faster.
BOTTOM LINE
AI design optimization with FEA works when a surrogate model replaces the full sweep: 12 DOE runs, a Gaussian process fit and 1 confirming run found the bracket section within 1.1% of the exact answer. Test it on a part with a known optimum first. Leo supplies the cited allowables and hand checks around the solver.
AI design optimization with FEA fits a surrogate model to a few solver runs, lets an optimizer search that surrogate, and confirms the winner with a real run. On the bracket below, that loop came within 1.1% of the exact optimum in 13 runs; a 1 mm grid search needed 1,326. It suits an engineer who owns the simulation step and can afford a few dozen runs per design review.
Grid sweeps spend most FEA runs on designs nobody will build
Take a cantilevered bracket with 2 free dimensions: section width b from 5 to 30 mm and height h from 10 to 60 mm. Sweeping both at 1 mm steps means 26 x 51 = 1,326 solver runs. At 20 minutes per run, a figure you should replace with your own solver time, that is 442 hours of compute for one load case.
Most of those runs land far from the answer. Of the 1,326 grid points, 712 break the stress or proportion limit, and 549 more carry over 50% more section area than the optimum. Only 65 runs fall anywhere near the design you would release.
Adding a third variable at 10 levels multiplies the run count by 10. That growth, not solver speed, is why teams freeze all but 1 or 2 dimensions and iterate by hand.
IN PRACTICE
Leo uses a Large Mechanical Model trained on 1M+ technical sources. It also provides citations, so we don't have to guess whether a material property or tolerance is correct. We see 96% accuracy on technical queries.
- Dorian G., AI Engineer
Surrogate-assisted optimization runs in 6 steps
The workflow below is the same whether you script it in Python or run it in a commercial process-integration tool.
Parameterize the CAD model so each design variable drives one dimension.
Pick a design of experiments (DOE). A Latin hypercube sample places exactly 1 point in each interval of each variable, so 12 points cover a 2-variable space evenly.
Run the FEA solver at every DOE point and record the outputs you care about (peak stress, deflection, mass).
Fit a surrogate model, such as a Gaussian process, that predicts each output from the inputs.
Run a constrained optimizer on the surrogate. The surrogate is cheap to evaluate, so the optimizer can call it thousands of times for the cost of zero solver runs.
Run the real solver at the optimizer's answer. If the result misses the surrogate's prediction by more than your tolerance, add that point as an infill point, refit, and repeat.
Commercial tools package these steps differently. The table lists what each vendor's own page states.
Tool | How it reduces solver runs | Stated data needs or limits |
|---|---|---|
Ansys optiSLang | Builds metamodels for fast feedback; an AI+ add-on uses AI for metamodeling | AI+ is an add-on to Pro, Premium or Enterprise licenses |
Siemens Simcenter HEEDS | SHERPA hybrid adaptive search; AI Simulation Predictor speeds it up | SHERPA needs no surrogates; Predictor saves up to 40% compute on long optimizations |
Dassault Systemes Isight | DOE, optimization and approximations around Abaqus and third-party solvers | Approximations are one of 4 listed techniques |
Ansys SimAI | Trains on past simulation results and geometry to predict new designs | Typically 30 to 100 results and about 2 days of training |
Sources: optiSLang, Simcenter HEEDS, Isight and SimAI. For the vendor side of the Ansys stack, see AI tools for Ansys simulation. If you need the shape itself to change rather than a few dimensions, topology optimization tools are the better fit.
Worked example: a 12-point DOE finds the bracket section in 13 runs
The goal: minimize the bracket's cross-section area b x h. The root bending stress must stay at or below 120 MPa, and h may not exceed 4b. The closed-form beam stress, 6FL/(bh^2), stands in for the FEA solver so you can rerun every step and check the answer exactly.
Input | Value | Where it comes from |
|---|---|---|
Tip load F | 2,000 N | Design load for this example |
Arm length L | 150 mm | Example geometry |
Allowable stress | 120 MPa | Set by your team from the material spec and safety factor |
Height-to-width limit | h at most 4b | Example manufacturing rule |
Bounds | b 5 to 30 mm, h 10 to 60 mm | Example design space |
The script ran these steps in Python with SciPy and scikit-learn:
Drew 12 Latin hypercube points across the bounds. Their stresses ranged from 26.9 MPa (b 21.0, h 56.4) to 1,011.6 MPa (b 6.6, h 16.5).
Fit a Gaussian process to the log of stress, which keeps the fit smooth across a stress range of nearly 38:1.
Ran the SLSQP optimizer on the surrogate from 4 start points with both constraints active.
Sent the best candidate, b 9.84 mm and h 39.36 mm, to the "solver" as run 13.
The surrogate predicted 120.0 MPa; the real calculation returned 118.1 MPa, a 1.6% miss and inside the limit, so the loop stopped.
Method | Solver runs | Best area | Stress at best design |
|---|---|---|---|
Exact solution (h = 4b, stress = 120 MPa) | none | 383.2 mm² (b 9.79, h 39.15) | 120.0 MPa |
1 mm grid sweep | 1,326 | 390 mm² (b 10, h 39) | 118.3 MPa |
Surrogate loop | 13 | 387.3 mm² (b 9.84, h 39.36) | 118.1 MPa |
At 20 minutes per run, the surrogate loop takes 4.3 hours against 442 hours for the sweep, and it beats the sweep's best area by 2.7 mm². A real FEA model adds mesh noise that a closed-form equation does not have, so budget a few extra infill runs and check the miss after each one.
Five tests show whether a surrogate works on your parts
Run these in one week on a part your team has already analysed by hand:
Known answer. Re-solve a past study whose optimum you trust. Pass: the surrogate's final design is within 2% of that objective and meets every constraint in a real solver run.
Hold-out accuracy. Leave 20% of the DOE points out of the fit. Pass: predicted peak stress is within 5% of the solver at each held-out point.
Run budget. Count every solver call, including infill runs. Pass: total runs stay under 10% of what a full sweep at your usual step size would need.
Mesh check at the final design. Refine the mesh in the peak-stress region once. Pass: peak stress changes by less than 3%.
Out-of-range query. Ask the surrogate about a design outside the DOE bounds. Pass: the tool warns you; SimAI, for example, reports a confidence level when a design is too far from its training data.
Gaussian processes slow down when the variable count passes a few dozen, per the scikit-learn documentation. Above that, screen variables first: optiSLang's sensitivity analysis exists for this, and it cuts the list to the dimensions that move the result.
Leo checks the inputs and the answer around the solver
An optimizer is only as good as its allowable stress, load case and material data, and Leo works on those inputs. Ask Leo a question such as "what allowable should we use for this 6061-T6 bracket under cyclic load, per our internal design standard?" It reads the standard and past calculation files your team connected from PDM, PLM or network drives, then returns a cited allowable and a calculation document you can attach to the study.
After the run, give Leo the final dimensions and load. It recomputes the hand check (here 6FL/(bh^2) at b 9.84 mm and h 39.36 mm gives 118 MPa) so a reviewer can compare it with the FEA peak before sign-off. Leo's part search can also find a bracket your company already released with a similar section, which may remove the study entirely.
One limit: Leo does not run FEA or CFD itself. It reads simulation results and tells you when a case needs a solver run. The engineering calculations guide shows more of those checks, and data handling is described on the security page.
FAQ
Ansys optiSLang: Process Integration and Design Optimization Software, Ansys (Synopsys), accessed 2026-11-10
Simcenter HEEDS, Siemens, accessed 2026-11-10
Isight and the SIMULIA Execution Engine, Dassault Systemes, accessed 2026-11-10
Ansys SimAI, Ansys (Synopsys), accessed 2026-11-10
Gaussian Processes, scikit-learn documentation, accessed 2026-11-10
scipy.stats.qmc.LatinHypercube, SciPy documentation, accessed 2026-11-10
Leo AI FAQ, Leo AI, accessed 2026-11-10
Check your FEA inputs with Leo
Ask an applications engineer how Leo fits your simulation setup.
Bring a bracket or housing from your own CAD. We will show Leo citing allowables from your standards, checking a hand calculation and finding similar released parts.
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