1. Course overview

This course addresses a practical engineering problem: crashworthiness and impact simulations in LS-DYNA are computationally expensive, and the design spaces we need to explore are large, nonlinear, and often noisy. A single explicit dynamic run of a full vehicle frontal impact model can take hours to days on a compute cluster, and a conventional full-factorial or Latin hypercube DOE with dozens of variables may require hundreds or thousands of runs. Most of those runs are wasted — they sample regions of the design space that are either infeasible, already well understood, or irrelevant to the response surface near the optimum. Active learning and adaptive design of experiments invert this logic: instead of committing to a fixed sampling plan up front, the algorithm sequentially selects the next simulation point based on what it has already learned, concentrating the computational budget where it reduces uncertainty or improves the predicted optimum most.

The scope of the course spans four connected layers. First, the statistical foundations: Gaussian process regression (Kriging), acquisition functions such as Expected Improvement (EI) and Lower Confidence Bound (LCB), and the distinction between exploration and exploitation. Second, the adaptive DOE mechanics: how a sequential sampler proposes candidates, how infill criteria are evaluated, how convergence is declared, and how constraints and failed runs are handled. Third, the LS-DYNA integration context: how parameters are injected into keyword decks, how runs are dispatched and monitored, how responses are extracted from binary databases, and how the surrogate model is coupled to the solver loop. Fourth, the engineering workflow: problem formulation, variable screening, surrogate validation, multi-objective trade-off analysis, and robustness checks before a design is released.

Why this matters in practice. A typical adaptive DOE campaign on a crash model with 8–12 design variables and a budget of 60–120 LS-DYNA runs can produce a surrogate with acceptable predictive accuracy (normalized RMSE below roughly 5–8% on a held-out validation set) and identify Pareto-optimal designs that a 40-run Latin hypercube would miss entirely. The savings are not merely computational; they change what questions an engineer can afford to ask.

The core loop: from fixed sampling to sequential learning

The essential difference between classical and adaptive DOE is where the decision-making happens. In a classical DOE, the sample locations are fixed before the first simulation starts. In an adaptive DOE, each new sample is chosen by solving a small optimization problem over the surrogate model's predictive distribution. The figure below shows the closed loop that connects the LS-DYNA solver, the response database, the surrogate, and the acquisition optimizer.

Adaptive DOE closed loop integrated with LS-DYNA A closed-loop diagram showing initial DOE sampling, LS-DYNA batch execution, response extraction, surrogate fitting, acquisition function optimization, infill point selection, convergence check, and final design recommendation. Initial DOE Latin hypercube, n₀ = 20 8 design variables LS-DYNA Batch *PARAMETER injection MPP solver, 32 cores Response Extraction d3plot → peak force, intrusion, mass, HIC Surrogate Kriging / GP fit + cross-validate Acquisition max EI(x) / LCB constrained by g(x)≤0 Infill Point x* new design vector written to run deck Convergence Check ΔEI < ε or budget reached? Design Release Pareto set, robust optimum, validation next iteration (if not converged) Budget accounting: n₀ = 20 initial runs + k infill runs (typically 15–40) = total 35–60 LS-DYNA jobs, versus 200+ for a comparable fixed LHS design. Each infill iteration adds one (or a small batch of) simulation(s); the surrogate is refit before the next acquisition step.

Read the loop clockwise from the top left. The initial DOE establishes a first surrogate. The acquisition function then scores every candidate point in the design space by a trade-off between predicted mean and predicted variance. The winning candidate is written into the LS-DYNA input deck, executed, and its responses are appended to the database. The surrogate is refit, and the cycle repeats until the acquisition improvement falls below a threshold or the run budget is exhausted. The dashed feedback arrow is the defining feature: the experiment is designed while it is being run.

What "active learning" means here, precisely

Active learning in this context is not a vague synonym for "smart sampling." It refers to a specific decision rule: at each iteration, select the input x that maximizes an acquisition function a(x) derived from the current posterior distribution. For a minimization problem with a Kriging surrogate having predicted mean μ(x) and standard deviation σ(x), the Expected Improvement criterion is

EI(x) = (f_min - μ(x)) · Φ(z) + σ(x) · φ(z),   z = (f_min - μ(x)) / σ(x)

where  f_min = best observed response so far
       Φ    = standard normal CDF
       φ    = standard normal PDF

The first term rewards points with a low predicted mean (exploitation); the second term rewards points with high uncertainty (exploration). This automatic balance is why active learning outperforms fixed sampling on expensive, smooth-but-nonlinear responses such as crash force–time curves. In LS-DYNA terms, the response might be the peak longitudinal deceleration at the B-pillar, the maximum intrusion into the occupant compartment, or the total mass of the front-end structure — each of which is a scalar extracted from a d3plot or nodout database after the run completes.

The LS-DYNA integration context

Coupling an adaptive DOE driver to LS-DYNA requires solving four concrete engineering problems, and the course treats each as a first-class topic.

  • Parameterization. Design variables must be expressed as *PARAMETER entries in the keyword deck (for example, t_rail, rib_spacing, gauge_front) so that a driver script can rewrite them without touching geometry. Variables that require re-meshing are handled through morphing or a parametric CAD-to-mesh pipeline, which is slower and must be budgeted accordingly.
  • Execution and monitoring. Runs are dispatched as batch jobs (typically via ls-dyna_mpp with a specified number of cores), and the driver must detect normal termination, negative-volume errors, and time-step collapse. Failed runs are not simply discarded; they are recorded and the surrogate is trained with a feasibility classifier or a penalized response.
  • Response extraction. Post-processing scripts read binary outputs — d3plot for nodal and element time histories, nodout for rigid-wall and accelerometer data, glstat for energy balance — and reduce them to the scalar objectives and constraints the optimizer needs. Energy-ratio checks (hourglass energy below 5% of internal energy, added mass below 1%) are applied here as run-quality gates.
  • Surrogate and optimizer coupling. The Kriging model, acquisition optimizer, and constraint handling live in a scripting layer (Python with a Gaussian-process library, or a commercial DOE tool) that calls the LS-DYNA driver as a black-box function.
Practical framing. Treat the LS-DYNA model as a deterministic black-box function f(x) → y that costs 2–12 wall-clock hours per evaluation. Every design decision in the adaptive loop — batch size, convergence tolerance, constraint handling — should be justified by that cost structure. A tolerance that saves three infill runs but risks a 10% error in the predicted optimum is a bad trade.

Engineering motivation and what you will be able to do

The motivation is straightforward: crash and impact design is a constrained multi-objective problem (minimize intrusion and peak acceleration, subject to mass and packaging limits), the feasible region is narrow, and simulation cost dominates the project schedule. Adaptive DOE lets a team reach a defensible design recommendation within a fixed run budget and, equally important, quantify the confidence in that recommendation through the surrogate's predictive variance. By the end of the course you will be able to formulate a parameterized LS-DYNA DOE problem, configure an adaptive sampling campaign with appropriate acquisition and convergence settings, validate the resulting surrogate against held-out simulations, and interpret the Pareto front and uncertainty estimates well enough to support a design review.

Scope boundary. This course assumes familiarity with LS-DYNA keyword input and basic explicit dynamics. It does not teach LS-DYNA from scratch, nor does it cover topology optimization or implicit forming simulations. The statistical content is developed from the engineering-use perspective: enough theory to choose and tune the method correctly, not a full derivation of Gaussian process mathematics.
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