3. Designing simulation cases for AI training data

An AI model trained on LS-DYNA results is only as trustworthy as the simulation cases that produced its labels. A dataset of ten thousand near-identical frontal crash runs teaches a surrogate model almost nothing about oblique loading, and a dataset that samples every parameter uniformly across physically impossible combinations wastes solver time on configurations no engineer would ever build. Case design is therefore a deliberate engineering activity: define the parameter space, choose a sampling strategy that covers it efficiently, and quantify how well the resulting dataset spans the space before a single training epoch is run.

Defining the Parameter Space

The parameter space is the Cartesian product of every input variable the model will see, each with a physically meaningful range and a documented distribution. For an LS-DYNA crashworthiness study, a typical space might include impact velocity, impact angle, barrier offset, sheet-gauge thickness, material yield stress, and strain-rate sensitivity. Each variable needs four attributes recorded in a machine-readable manifest: name, unit, lower bound, upper bound, and sampling distribution. Units are not cosmetic — mixing millimetres and metres between the pre-processor and the sampling script is one of the most common causes of silently invalid datasets.

Bounds must be justified by physics and by the intended deployment envelope, not chosen for convenience. If the target application is a vehicle rated for 30–64 km/h frontal impacts, sampling velocity up to 120 km/h produces cases that are expensive to solve and irrelevant to the model's operating domain. Conversely, clipping the range too tightly creates a model that fails at the edges of its envelope. A practical rule is to set the training bounds slightly wider than the deployment envelope — typically 10–15% — so the model interpolates rather than extrapolates at the boundary.

Correlated parameters deserve explicit treatment. Thickness and material grade are often linked by a design catalogue; sampling them independently generates combinations that cannot be manufactured. Where such constraints exist, encode them as a feasibility predicate evaluated after sampling, and record the rejection rate. A rejection rate above roughly 30% signals that the sampling strategy, not the constraint, should be redesigned.

Design of Experiments for Solver-Backed Datasets

Classical design of experiments (DoE) was developed for physical tests where each run is costly and noise is significant. LS-DYNA runs are deterministic given identical input decks, so the dominant cost is wall-clock time, and the dominant risk is poor coverage rather than measurement noise. This shifts the preferred methods toward space-filling designs.

Latin Hypercube Sampling (LHS) remains the workhorse. With n samples and k parameters, LHS divides each parameter's range into n equal-probability strata and places exactly one sample per stratum per dimension, then pairs the strata across dimensions randomly. This guarantees marginal coverage in every dimension while keeping the total run count linear in n. A 200-run LHS over six parameters is a reasonable starting budget for a surrogate model of global crash response.

Maximin LHS improves on plain LHS by optimizing the random pairing to maximize the minimum pairwise distance between samples, which reduces clustering in the joint space. It costs a few seconds of computation and typically improves coverage metrics measurably. Sobol sequences offer low-discrepancy coverage and are preferable when the dataset will later support variance-based sensitivity analysis, because their structure permits Sobol index estimation without a separate design.

Pure space-filling designs, however, ignore regions of high nonlinearity. A hybrid strategy is often best: seed the dataset with a maximin LHS of 150–200 runs for global coverage, then add 30–50 adaptive samples in regions where a cheap preliminary surrogate shows large prediction error or where the response surface has sharp gradients — for example, near the velocity threshold where a crash box transitions from progressive folding to global bending. Adaptive infill concentrates solver budget where the model most needs resolution.

# Example manifest entry (YAML) for one parameter
- name: impact_velocity
  unit: km/h
  lower: 25.0
  upper: 70.0
  distribution: uniform
  constraint: null
- name: sheet_gauge
  unit: mm
  lower: 0.8
  upper: 2.0
  distribution: uniform
  constraint: "sheet_gauge >= 0.0012 * yield_stress_MPa"

Coverage Metrics

Coverage cannot be asserted; it must be measured. Three complementary metrics are sufficient for most LS-DYNA training datasets.

Discrepancy quantifies deviation from uniform filling. The centred L2-discrepancy is cheap to compute and decreases as the design becomes more uniform; comparing the value for the generated design against a reference random design of the same size gives an immediate sanity check. Minimum inter-point distance (the maximin criterion) reports the tightest cluster in the normalized space; a small value relative to the space diagonal indicates redundant runs. Stratification coverage counts the fraction of occupied cells in a coarse grid — for six parameters, a 4⁶ = 4096-cell grid is tractable, and an occupancy of 60–80% for 200 samples is a healthy target.

Coverage must also be checked in the output space, not only the input space. Two input points far apart may produce nearly identical responses, and a dataset that is well spread in inputs but clustered in outputs will train a model that is accurate on average and blind to rare outcomes. Binning the scalar response (peak acceleration, intrusion, energy absorbed) into deciles and reporting the sample count per bin exposes this immediately. If the top decile of peak acceleration contains only three runs, the model will not learn the high-severity regime regardless of how elegant the input design is.

Worked Example: A Six-Parameter Frontal Impact Study

Consider a simplified frontal impact model with six inputs: impact velocity (25–70 km/h), impact angle (−15° to +15°), barrier offset (−300 to +300 mm), sheet gauge (0.8–2.0 mm), yield stress (280–420 MPa), and strain-rate parameter C (10–60). The target is a 220-run dataset. A maximin LHS generates 180 runs; the feasibility predicate rejects 14 combinations, leaving 166. Adaptive infill adds 40 runs concentrated where a preliminary kriging surrogate shows error above 8% — predominantly near 55 km/h, where the folding-to-bending transition occurs. The final 206-run dataset reports a centred L2-discrepancy 38% below a random design of equal size, a minimum normalized inter-point distance of 0.11, and 71% occupancy of the 4⁶ grid. Output decile counts range from 17 to 26 per bin, confirming that the high-severity regime is represented.

These figures are illustrative of a well-formed design, not measured results from a specific model; the point is that each metric is computed and recorded alongside the dataset so that coverage is auditable rather than assumed.

Recording the Design as a Deliverable

The design must ship with the dataset as a manifest, not live only in a notebook. A minimal manifest records the parameter table with units and bounds, the sampling method and random seed, the feasibility predicate, the rejection count, the infill criteria, and the final coverage metrics. With the seed and method recorded, the design is exactly reproducible; without them, a later reviewer cannot distinguish a deliberate sampling choice from an accident. The manifest is also the natural place to record the LS-DYNA version and solver settings, since a change in contact algorithm or time-step control can shift the response surface and invalidate the coverage assessment performed on an earlier solver build.

Two failure symptoms are worth recognizing early. If the minimum inter-point distance collapses after adding infill, the adaptive criterion is over-concentrating samples in one region and should be relaxed or capped. If output decile counts are badly skewed despite good input coverage, the response is dominated by a threshold effect that the input design does not resolve, and the parameter space itself — not the sampler — needs revisiting. Both are caught by the metrics above before any training run begins, which is precisely the point of measuring coverage rather than assuming it.