# Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation

arXiv: https://arxiv.org/abs/2106.13790 · HTML: https://mlsanity.com/paper/2106.13790/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 25 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [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)
- [Modern Monte Carlo Methods for Efficient Uncertainty Quantification and Propagation: A Survey](https://mlsanity.com/paper/2011.00680/) (2020)
- [Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence](https://mlsanity.com/paper/1811.09757/) (2018)
- [Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes](https://mlsanity.com/paper/2006.15924/) (2020)
- [Adaptive Physics-Informed Neural Networks for Markov-Chain Monte Carlo](https://mlsanity.com/paper/2008.01604/) (2020)
- [Multifidelity probability estimation via fusion of estimators](https://mlsanity.com/paper/1905.02679/) (2019)
- [Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling](https://mlsanity.com/paper/2101.02786/) (2021)
- [Inverse modeling of hydrologic systems with adaptive multi-fidelity Markov chain Monte Carlo simulations](https://mlsanity.com/paper/1712.02070/) (2017)

## Built on by (most cited first, 8 of 8)

- [A Comprehensive Survey on Rare Event Prediction](https://mlsanity.com/paper/2309.11356/) (2023)
- [Cost-effective Framework for Gradual Domain Adaptation with Multifidelity](https://mlsanity.com/paper/2202.04359/) (2022)
- [Bayesian Inference with Latent Hamiltonian Neural Networks](https://mlsanity.com/paper/2208.06120/) (2022)
- [Reliability Analysis of Complex Systems using Subset Simulations with Hamiltonian Neural Networks](https://mlsanity.com/paper/2401.05244/) (2024)
- [Active Learning with Bayesian Multi-Fidelity Laplace Neural Operators for Oscillatory Parametric PDEs](https://mlsanity.com/paper/2502.00550/) (2025)
- [Reliability Estimation of an Advanced Nuclear Fuel using Coupled Active Learning, Multifidelity Modeling, and Subset Simulation](https://mlsanity.com/paper/2201.02172/) (2022)
- [General multi-fidelity surrogate models: Framework and active learning strategies for efficient rare event simulation](https://mlsanity.com/paper/2212.03375/) (2022)
- [Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference](https://mlsanity.com/paper/2209.09349/) (2022)

## Abstract (arXiv)

While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies and two finite element (FE) model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.