# Enhancing Polynomial Chaos Expansion Based Surrogate Modeling using a Novel Probabilistic Transfer Learning Strategy

arXiv: https://arxiv.org/abs/2312.04648 · HTML: https://mlsanity.com/paper/2312.04648/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 45 references that are in the map.
- First posted on arXiv 7 Dec 2023.

## Builds on (most cited first, 5 of 5)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [A Survey on Deep Transfer Learning](https://mlsanity.com/paper/1808.01974/) (2018)

## Built on by (most cited first, 1 of 1)

- [Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy](https://mlsanity.com/paper/2412.11875/) (2024)

## Abstract (arXiv)

In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations, non-intrusive PCE allows the construction of these surrogates using a set of simulation response evaluations. In this context, the PCE coefficients can be obtained using linear regression, which is also known as point collocation or stochastic response surfaces. Regression exhibits better scalability and can handle noisy function evaluations in contrast to other non-intrusive approaches, such as projection. However, since over-sampling is generally advisable for the linear regression approach, the simulation requirements become prohibitive for expensive forward models. We propose to leverage transfer learning whereby knowledge gained through similar PCE surrogate construction tasks (source domains) is transferred to a new surrogate-construction task (target domain) which has a limited number of forward model simulations (training data). The proposed transfer learning strategy determines how much, if any, information to transfer using new techniques inspired by Bayesian modeling and data assimilation. The strategy is scrutinized using numerical investigations and applied to an engineering problem from the oil and gas industry.