# An hp-adaptive multi-element stochastic collocation method for surrogate modeling with information re-use

arXiv: https://arxiv.org/abs/2206.14435 · HTML: https://mlsanity.com/paper/2206.14435/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2022.

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

- [Physics-Informed Polynomial Chaos Expansions](https://mlsanity.com/paper/2309.01697/) (2023)
- [Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion](https://mlsanity.com/paper/2301.13635/) (2023)
- [Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling](https://mlsanity.com/paper/2510.22375/) (2025)

## Abstract (arXiv)

This paper introduces an hp-adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either h- or p-refinement. The collocation method is based on weighted Leja nodes. After h-refinement, local interpolations are stabilized by adding and sorting Leja nodes on each newly created sub-element in a hierarchical manner. For p-refinement, the local polynomial approximations are based on total-degree or dimension-adaptive bases. The method is applied in the context of forward and inverse uncertainty quantification to handle non-smooth or strongly localised response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods.