# On the Correspondence between Gaussian Processes and Geometric Harmonics

arXiv: https://arxiv.org/abs/2110.02296 · HTML: https://mlsanity.com/paper/2110.02296/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 55 references that are in the map.
- First posted on arXiv 5 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration](https://mlsanity.com/paper/1801.00203/) (2017)
- [Neural-net-induced Gaussian process regression for function approximation and PDE solution](https://mlsanity.com/paper/1806.11187/) (2018)
- [Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updates](https://mlsanity.com/paper/2102.03646/) (2021)
- [Learning to Forecast Dynamical Systems from Streaming Data](https://mlsanity.com/paper/2109.09703/) (2021)
- [Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets](https://mlsanity.com/paper/2010.14324/) (2020)
- [Landmark Diffusion Maps (L-dMaps): Accelerated manifold learning out-of-sample extension](https://mlsanity.com/paper/1706.09396/) (2017)
- [Gaussian Process Landmarking on Manifolds](https://mlsanity.com/paper/1802.03479/) (2018)
- [Selecting the independent coordinates of manifolds with large aspect ratios](https://mlsanity.com/paper/1907.01651/) (2019)
- [Probabilistic Learning on Manifolds (PLoM) with Partition](https://mlsanity.com/paper/2102.10894/) (2021)
- [Conditional Karhunen-Lo`eve expansion for uncertainty quantification and active learning in partial differential equation models](https://mlsanity.com/paper/1904.08069/) (2019)
- [Manifold Learning for Accelerating Coarse-Grained Optimization](https://mlsanity.com/paper/2001.03518/) (2020)
- [Gaussian Process Regression for Out-of-Sample Extension](https://mlsanity.com/paper/1603.02194/) (2016)

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

- [GANs and Closures: Micro-Macro Consistency in Multiscale Modeling](https://mlsanity.com/paper/2208.10715/) (2022)
- [On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among them](https://mlsanity.com/paper/2406.06812/) (2024)
- [On-Manifold Projected Gradient Descent](https://mlsanity.com/paper/2308.12279/) (2023)

## Abstract (arXiv)

We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue different goals. Results from both camps can be successfully combined, providing alternative interpretations of uncertainty in terms of error estimation, or leading towards accelerated Bayesian Optimization due to dimensionality reduction.