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To fit a simulation with fewer experiments, first define whether you need parameter calibration, prediction, sensitivity analysis, optimization, or validation. Then screen the inputs, choose test points for that purpose, use a metamodel or sequential design only where it helps, and reserve independent data to test predictive accuracy. There is no evidence-backed universal number of experiments saved: the right reduction depends on the model, experiment cost, noise, and objective.
Decide what “fit” means before choosing experiments
“Fit” can mean setting model parameters to match observations, or it can mean building confidence that the simulation predicts a real process. Those are different tasks, and they call for different data.
- Calibration: use observed data to estimate or set model parameters.
- Sensitivity analysis: identify which inputs materially affect outputs.
- Optimization: find input settings that improve a defined outcome.
- Prediction or validation: assess how accurately the model and its implementation predict a characterized process.
State the output you care about, the input ranges you can test, and the decision the simulation must support. The design and analysis should serve that purpose, rather than simply collecting more points. Kleijnen’s tutorial discusses simulation-experiment design across such goals: Design and Analysis of Simulation Experiments: Tutorial.
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Screen inputs before detailed modeling
If a simulation has many adjustable inputs, begin by determining which ones appear important. Screening can reduce the factor set before spending effort on a detailed response model. It does not prove that excluded factors never matter; interactions or a narrower operating region may change their influence.
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For planned test points, classical designs such as fractional factorial designs can examine factors efficiently, while optimal designs can target a chosen model or objective. Designs that account for interactions matter when one input’s effect may depend on another. Avoid replacing a designed plan with arbitrary sampling: ad hoc points may leave important regions or combinations unexamined. Kleijnen’s discussion of sensitivity analysis, optimization, and validation covers screening and design options: Experimental Design for Sensitivity Analysis, Optimization and Validation of Simulation Models.
Use a metamodel as a fast approximation
A metamodel approximates the simulation’s input-output behavior, allowing you to explore or optimize without running the full model at every candidate setting. Low-order polynomial regression and Kriging, also called Gaussian-process modeling, are two families discussed in the literature. The approximation is not the physical system and does not make the original simulation correct.
Choose the metamodel and its test-point design together. Check predictive adequacy and uncertainty in the regions where you plan to make decisions; a smooth-looking approximation alone is not evidence that it is reliable. The Kleijnen tutorial explains the connection between metamodel choice, design, and input screening. MathWorks describes one software example involving test-point design, space-filling designs, Gaussian-process response models, and a convex-hull boundary in its R2026b Design of Experiments overview. That documentation describes a specific toolbox workflow, not a universally best method.
For expensive simulations, consider sequential design
When each simulation run is costly, sequential Bayesian experimental design can use earlier outputs to choose the next parameter setting. A 2024 article abstract describes an emulator and a selection criterion that balances exploration in uncertain posterior regions with exploitation in high-posterior-density regions: Sequential Bayesian Experimental Design for Calibration of Expensive Simulation Models. This is a strategy for choosing runs, not a guaranteed reduction in experiment count.
Keep calibration separate from validation
Calibration uses data to set parameters; validation experiments assess predictive accuracy for a characterized physical process. A model that matches the data used to fit it has not thereby demonstrated that it predicts new conditions accurately. Reserve independent observations or test conditions for validation when predictive performance is the goal.
A Cambridge University Press chapter describes validation experiments as designed, executed, and analyzed to determine predictive accuracy for a well-characterized process: Design and execution of validation experiments.
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Account for simulation error and uncertainty
A useful experiment plan considers uncertainty and error alongside the choice of test points. NIST’s 2005 publication frames verification and validation around error analysis, experimental design, and uncertainty analysis; it also discusses randomized or orthogonal designs for evaluating interactions and the use of standard reference benchmarks. See A B C of Statistics for Verification and Validation of Simulations of High-Consequence Engineering Systems.
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For stochastic simulations, variance-reduction techniques may help compare alternatives more precisely. The methods discussed in the Tilburg University record include common pseudorandom numbers, antithetic numbers, control variates or regression sampling, and importance sampling. These apply to simulation-output analysis where their assumptions fit; they are not blanket prescriptions for reducing physical experiments.
Choose a method against your constraints
There is no single design or metamodel that wins for every project. Compare options against the question being answered, the number and type of inputs, observation noise and cost, simulation runtime, uncertainty treatment, and whether independent validation data are available. A method that saves costly simulation runs may not reduce the number of physical measurements you need.
- For many inputs and an unclear set of influential factors, start with screening.
- For estimating effects or interactions, use a structured design suited to the factors and response model.
- For exploring or optimizing a costly model, consider a checked metamodel or sequential design.
- For claims about predictive accuracy, prioritize independent validation conditions and uncertainty analysis.
The cited sources support these approaches but do not establish a universal speed-up, cost reduction, or number of experiments saved. Any such figure needs a specific application, method, baseline, and study.
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