# Actively Learning Joint Contours of Multiple Computer Experiments

arXiv: https://arxiv.org/abs/2512.13530 · HTML: https://mlsanity.com/paper/2512.13530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 17 of 17)

- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [Sequential Learning of Active Subspaces](https://mlsanity.com/paper/1907.11572/) (2019)
- [Deep Gaussian Process Emulation using Stochastic Imputation](https://mlsanity.com/paper/2107.01590/) (2021)
- [Triangulation candidates for Bayesian optimization](https://mlsanity.com/paper/2112.07457/) (2021)
- [Contour location via entropy reduction leveraging multiple information sources](https://mlsanity.com/paper/1805.07489/) (2018)
- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [Nonstationary Gaussian Process Surrogates](https://mlsanity.com/paper/2305.19242/) (2023)
- [Contour Location for Reliability in Airfoil Simulation Experiments using Deep Gaussian Processes](https://mlsanity.com/paper/2308.04420/) (2023)
- [Voronoi Candidates for Bayesian Optimization](https://mlsanity.com/paper/2402.04922/) (2024)
- [Active Learning for Derivative-Based Global Sensitivity Analysis with Gaussian Processes](https://mlsanity.com/paper/2407.09739/) (2024)
- [Targeted Adaptive Design](https://mlsanity.com/paper/2205.14208/) (2022)
- [Augmenting a simulation campaign for hybrid computer model and field data experiments](https://mlsanity.com/paper/2301.10228/) (2023)
- [Simulation Experiment Design for Calibration via Active Learning](https://mlsanity.com/paper/2407.18885/) (2024)
- [Deep Gaussian Process Emulation and Uncertainty Quantification for Large Computer Experiments](https://mlsanity.com/paper/2411.14690/) (2024)
- [Efficient Active Learning Strategies for Computer Experiments](https://mlsanity.com/paper/2501.13841/) (2025)

## Abstract (arXiv)

Contour location---the process of sequentially training a surrogate model to identify the design inputs that result in a pre-specified response value from a single computer experiment---is a well-studied active learning problem. Here, we tackle a related but distinct problem: identifying the input configuration that returns pre-specified values of multiple computer experiments simultaneously. Motivated by computer experiments of the rotational torques acting upon a vehicle in flight, we aim to identify stable flight conditions that result in zero torque forces. We propose a ``joint contour location'' (jCL) scheme that strikes a strategic balance between exploring the multiple response surfaces while exploiting learning of the intersecting contours. Rather than working exploration and exploitation into a single acquisition function, we devise two distinct acquisition schemes with a decision rule to choose between the two, which also provides a natural stopping criterion if no solution is present. We employ traditional Gaussian processes (GPs), multitask GPs, and deep GPs, but our jCL procedure is applicable to any surrogate that can provide posterior predictive distributions. Our jCL designs significantly outperform existing (single response) CL strategies, optimization-based alternatives, and previous strategies for targeting joint contours, enabling us to efficiently locate the optimal configurations for our motivating computer experiments.