# A few-shot graph Laplacian-based approach for improving the accuracy of low-fidelity data

arXiv: https://arxiv.org/abs/2304.04862 · HTML: https://mlsanity.com/paper/2304.04862/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator](https://mlsanity.com/paper/1801.10108/) (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)
- [Multi-Fidelity Bayesian Optimization via Deep Neural Networks](https://mlsanity.com/paper/2007.03117/) (2020)
- [Analysis of p-Laplacian Regularization in Semi-Supervised Learning](https://mlsanity.com/paper/1707.06213/) (2017)
- [A variational approach to the consistency of spectral clustering](https://mlsanity.com/paper/1508.01928/) (2015)
- [On transfer learning of neural networks using bi-fidelity data for uncertainty propagation](https://mlsanity.com/paper/2002.04495/) (2020)
- [Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)](https://mlsanity.com/paper/2106.13361/) (2021)
- [Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms](https://mlsanity.com/paper/1805.09450/) (2018)
- [Multi-fidelity Generative Deep Learning Turbulent Flows](https://mlsanity.com/paper/2006.04731/) (2020)
- [Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods](https://mlsanity.com/paper/1906.07658/) (2019)
- [Posterior Consistency of Semi-Supervised Regression on Graphs](https://mlsanity.com/paper/2007.12809/) (2020)

## Abstract (arXiv)

Low-fidelity data is typically inexpensive to generate but inaccurate. On the other hand, high-fidelity data is accurate but expensive to obtain. Multi-fidelity methods use a small set of high-fidelity data to enhance the accuracy of a large set of low-fidelity data. In the approach described in this paper, this is accomplished by constructing a graph Laplacian using the low-fidelity data and computing its low-lying spectrum. This spectrum is then used to cluster the data and identify points that are closest to the centroids of the clusters. High-fidelity data is then acquired for these key points. Thereafter, a transformation that maps every low-fidelity data point to its bi-fidelity counterpart is determined by minimizing the discrepancy between the bi- and high-fidelity data at the key points, and to preserve the underlying structure of the low-fidelity data distribution. The latter objective is achieved by relying, once again, on the spectral properties of the graph Laplacian. This method is applied to a problem in solid mechanics and another in aerodynamics. In both cases, this methods uses a small fraction of high-fidelity data to significantly improve the accuracy of a large set of low-fidelity data.