# Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification

arXiv: https://arxiv.org/abs/2211.10835 · HTML: https://mlsanity.com/paper/2211.10835/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 20 Nov 2022.

## 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)
- [On transfer learning of neural networks using bi-fidelity data for uncertainty propagation](https://mlsanity.com/paper/2002.04495/) (2020)
- [MFNets: Data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources](https://mlsanity.com/paper/2008.02672/) (2020)
- [Context-aware surrogate modeling for balancing approximation and sampling costs in multi-fidelity importance sampling and Bayesian inverse problems](https://mlsanity.com/paper/2010.11708/) (2020)
- [A general framework for quantifying uncertainty at scale](https://mlsanity.com/paper/2202.03999/) (2022)
- [Context-aware controller inference for stabilizing dynamical systems from scarce data](https://mlsanity.com/paper/2207.11049/) (2022)
- [A bandit-learning approach to multifidelity approximation](https://mlsanity.com/paper/2103.15342/) (2021)
- [Sensitivity-driven adaptive sparse stochastic approximations in plasma microinstability analysis](https://mlsanity.com/paper/1812.00080/) (2018)
- [Control Variate Polynomial Chaos: Optimal Fusion of Sampling and Surrogates for Multifidelity Uncertainty Quantification](https://mlsanity.com/paper/2201.10745/) (2022)
- [A Multifidelity Monte Carlo Method for Realistic Computational Budgets](https://mlsanity.com/paper/2206.07572/) (2022)

## Built on by (most cited first, 3 of 3)

- [A DeepONet multi-fidelity approach for residual learning in reduced order modeling](https://mlsanity.com/paper/2302.12682/) (2023)
- [Multi-fidelity Gaussian process surrogate modeling for regression problems in physics](https://mlsanity.com/paper/2404.11965/) (2024)
- [Multifidelity linear regression for scientific machine learning from scarce data](https://mlsanity.com/paper/2403.08627/) (2024)

## Abstract (arXiv)

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. It generalizes the previously developed context-aware bi-fidelity Monte Carlo method to hierarchies of multiple models and to more general types of low-fidelity models. When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets. This is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs and typically ignore the context in which the learned models will be used in upstream tasks. The proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies of a wide range of types of low-fidelity models such as sparse-grid and deep-network models. Numerical experiments with the gyrokinetic simulation code textscGene show speedups of up to two orders of magnitude compared to standard estimators when quantifying uncertainties in small-scale fluctuations in confined plasma in fusion reactors. This corresponds to a runtime reduction from 72 days to about four hours on one node of the Lonestar6 supercomputer at the Texas Advanced Computing Center.