# Replication or exploration? Sequential design for stochastic simulation experiments

arXiv: https://arxiv.org/abs/1710.03206 · HTML: https://mlsanity.com/paper/1710.03206/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2017.

## Built on by (most cited first, 30 of 30)

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- [Batch Bayesian Optimization for Replicable Experimental Design](https://mlsanity.com/paper/2311.01195/) (2023)
- [Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma](https://mlsanity.com/paper/2306.07299/) (2023)
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- [Facilitating automated conversion of scientific knowledge into scientific simulation models with the Machine Assisted Generation, Calibration, and Comparison (MAGCC) Framework](https://mlsanity.com/paper/2204.10382/) (2022)
- [Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method](https://mlsanity.com/paper/2207.03842/) (2022)
- [Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processes](https://mlsanity.com/paper/2405.10581/) (2024)
- [Gearing Gaussian process modeling and sequential design towards stochastic simulators](https://mlsanity.com/paper/2412.07306/) (2024)
- [Multi-objective hyperparameter optimization with performance uncertainty](https://mlsanity.com/paper/2209.04340/) (2022)
- [Sensitivity Analysis in the Presence of Intrinsic Stochasticity for Discrete Fracture Network Simulations](https://mlsanity.com/paper/2312.04722/) (2023)
- [Quantifying Local Model Validity using Active Learning](https://mlsanity.com/paper/2406.07474/) (2024)
- [Multifidelity Cross-validation](https://mlsanity.com/paper/2407.01495/) (2024)
- [Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions](https://mlsanity.com/paper/2504.20527/) (2025)
- [Active Learning for Manifold Gaussian Process Regression](https://mlsanity.com/paper/2506.20928/) (2025)
- [Deep Intrinsic Coregionalization Multi-Output Gaussian Process Surrogate with Active Learning](https://mlsanity.com/paper/2508.16434/) (2025)
- [Learning stochasticity: a nonparametric framework for intrinsic noise estimation](https://mlsanity.com/paper/2511.13701/) (2025)
- [Actively Learning Joint Contours of Multiple Computer Experiments](https://mlsanity.com/paper/2512.13530/) (2025)
- [Fast and Provably Accurate Sequential Designs using Hilbert Space Gaussian Processes](https://mlsanity.com/paper/2604.20414/) (2026)
- [Efficient Heteroscedastic Bayesian Optimization for Risk-Aware AutoRL](https://mlsanity.com/paper/2607.26680/) (2026)
- [When Repeated Measurements Hurt Tabular Foundation Models](https://mlsanity.com/paper/2610.16801/) (2026)
- [Principled Design of Expected Improvement for Continuous Simulation Optimization](https://mlsanity.com/paper/2610.18434/) (2026)

## Abstract (arXiv)

We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experiments. We first show that replication can be beneficial from both design and computational perspectives, in the context of Gaussian process surrogate modeling. We then develop a lookahead based sequential design scheme that can determine if a new run should be at an existing input location (i.e., replicate) or at a new one (explore). When paired with a newly developed heteroskedastic Gaussian process model, our dynamic design scheme facilitates learning of signal and noise relationships which can vary throughout the input space. We show that it does so efficiently, on both computational and statistical grounds. In addition to illustrative synthetic examples, we demonstrate performance on two challenging real-data simulation experiments, from inventory management and epidemiology.