# A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Sampling

arXiv: https://arxiv.org/abs/2310.03298 · HTML: https://mlsanity.com/paper/2310.03298/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 76 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 21 of 21)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [Multi-fidelity Bayesian Neural Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.13294/) (2020)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Multi-Fidelity Bayesian Optimization via Deep Neural Networks](https://mlsanity.com/paper/2007.03117/) (2020)
- [A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors](https://mlsanity.com/paper/1806.07504/) (2018)
- [Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities](https://mlsanity.com/paper/2006.16728/) (2020)
- [Deep Multi-Fidelity Active Learning of High-dimensional Outputs](https://mlsanity.com/paper/2012.00901/) (2020)
- [Multi-Fidelity Cost-Aware Bayesian Optimization](https://mlsanity.com/paper/2211.02732/) (2022)
- [Multi-fidelity surrogate modeling using long short-term memory networks](https://mlsanity.com/paper/2208.03115/) (2022)
- [Data Fusion with Latent Map Gaussian Processes](https://mlsanity.com/paper/2112.02206/) (2021)
- [A DeepONet multi-fidelity approach for residual learning in reduced order modeling](https://mlsanity.com/paper/2302.12682/) (2023)
- [Scalable Gaussian Processes for Data-Driven Design using Big Data with Categorical Factors](https://mlsanity.com/paper/2106.15356/) (2021)
- [Disentangled Multi-Fidelity Deep Bayesian Active Learning](https://mlsanity.com/paper/2305.04392/) (2023)
- [A Multi-Fidelity Active Learning Method for Global Design Optimization Problems with Noisy Evaluations](https://mlsanity.com/paper/2202.06902/) (2022)
- [Reduced-Order Multiscale Modeling of Plastic Deformations in 3D Alloys with Spatially Varying Porosity by Deflated Clustering Analysis](https://mlsanity.com/paper/2108.03742/) (2021)
- [General multi-fidelity surrogate models: Framework and active learning strategies for efficient rare event simulation](https://mlsanity.com/paper/2212.03375/) (2022)

## Built on by (most cited first, 10 of 10)

- [Real-Time Decision-Making for Digital Twin in Additive Manufacturing with Model Predictive Control using Time-Series Deep Neural Networks](https://mlsanity.com/paper/2501.07601/) (2025)
- [Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models](https://mlsanity.com/paper/2407.15110/) (2024)
- [Interpretable Multi-Source Data Fusion Through Latent Variable Gaussian Process](https://mlsanity.com/paper/2402.04146/) (2024)
- [Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives](https://mlsanity.com/paper/2603.12870/) (2026)
- [Heterogenous Multi-Source Data Fusion Through Input Mapping and Latent Variable Gaussian Process](https://mlsanity.com/paper/2407.11268/) (2024)
- [Emerging Microelectronic Materials by Design: Navigating Combinatorial Design Space with Scarce and Dispersed Data](https://mlsanity.com/paper/2412.17283/) (2024)
- [Adaptive Multi-Fidelity Reinforcement Learning for Variance Reduction in Engineering Design Optimization](https://mlsanity.com/paper/2503.18229/) (2025)
- [ARCO-BO: Adaptive Resource-aware COllaborative Bayesian Optimization for Heterogeneous Multi-Agent Design](https://mlsanity.com/paper/2510.16652/) (2025)
- [Digital Twin-based Control Co-Design of Full Vehicle Active Suspensions via Deep Reinforcement Learning](https://mlsanity.com/paper/2512.03891/) (2025)
- [Multi-task Modeling for Engineering Applications with Sparse Data](https://mlsanity.com/paper/2601.05910/) (2026)

## Abstract (arXiv)

Multi-fidelity (MF) methods are gaining popularity for enhancing surrogate modeling and design optimization by incorporating data from various low-fidelity (LF) models. While most existing MF methods assume a fixed dataset, adaptive sampling methods that dynamically allocate resources among fidelity models can achieve higher efficiency in the exploring and exploiting the design space. However, most existing MF methods rely on the hierarchical assumption of fidelity levels or fail to capture the intercorrelation between multiple fidelity levels and utilize it to quantify the value of the future samples and navigate the adaptive sampling. To address this hurdle, we propose a framework hinged on a latent embedding for different fidelity models and the associated pre-posterior analysis to explicitly utilize their correlation for adaptive sampling. In this framework, each infill sampling iteration includes two steps: We first identify the location of interest with the greatest potential improvement using the high-fidelity (HF) model, then we search for the next sample across all fidelity levels that maximize the improvement per unit cost at the location identified in the first step. This is made possible by a single Latent Variable Gaussian Process (LVGP) model that maps different fidelity models into an interpretable latent space to capture their correlations without assuming hierarchical fidelity levels. The LVGP enables us to assess how LF sampling candidates will affect HF response with pre-posterior analysis and determine the next sample with the best benefit-to-cost ratio. Through test cases, we demonstrate that the proposed method outperforms the benchmark methods in both MF global fitting (GF) and Bayesian Optimization (BO) problems in convergence rate and robustness. Moreover, the method offers the flexibility to switch between GF and BO by simply changing the acquisition function.