# A machine learning approach for efficient uncertainty quantification using multiscale methods

arXiv: https://arxiv.org/abs/1711.04315 · HTML: https://mlsanity.com/paper/1711.04315/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2017.

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

- [Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems](https://mlsanity.com/paper/2203.00003/) (2022)
- [Predicting Mechanically Driven Full-Field Quantities of Interest with Deep Learning-Based Metamodels](https://mlsanity.com/paper/2108.03995/) (2021)
- [A Bayesian Multiscale Deep Learning Framework for Flows in Random Media](https://mlsanity.com/paper/2103.09056/) (2021)
- [Deep-learning-based upscaling method for geologic models via theory-guided convolutional neural network](https://mlsanity.com/paper/2201.00698/) (2021)
- [Uncertainty quantification of two-phase flow in porous media via coupled-TgNN surrogate model](https://mlsanity.com/paper/2205.14301/) (2022)
- [Physics-Aware Neural Networks for Boundary Layer Linear Problems](https://mlsanity.com/paper/2208.12559/) (2022)
- [UQ of 2D Slab Burner DNS: Surrogates, Uncertainty Propagation, and Parameter Calibration](https://mlsanity.com/paper/2411.16693/) (2024)
- [Machine learning for sustainable geoenergy: uncertainty, physics and decision-ready inference](https://mlsanity.com/paper/2603.14907/) (2026)

## Abstract (arXiv)

Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these coarse scale basis functions. Specifically, we employ a neural network predictor fitted using a set of solution samples from which it learns to generate subsequent basis functions at a lower computational cost than solving the local problems. The computational advantage of this approach is realized for uncertainty quantification tasks where a large number of realizations has to be evaluated. We attribute the ability to learn these basis functions to the modularity of the local problems and the redundancy of the permeability patches between samples. The proposed method is evaluated on elliptic problems yielding very promising results.