# Gaussian Process Manifold Interpolation for Probabilistic Atrial Activation Maps and Uncertain Conduction Velocity

arXiv: https://arxiv.org/abs/2004.10586 · HTML: https://mlsanity.com/paper/2004.10586/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2020.

## Built on by (most cited first, 13 of 13)

- [Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case](https://mlsanity.com/paper/2208.14960/) (2022)
- [Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces](https://mlsanity.com/paper/2301.13088/) (2023)
- [Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps](https://mlsanity.com/paper/2201.12362/) (2022)
- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks](https://mlsanity.com/paper/2102.10863/) (2021)
- [Intrinsic Gaussian Vector Fields on Manifolds](https://mlsanity.com/paper/2310.18824/) (2023)
- [Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifolds](https://mlsanity.com/paper/2309.10918/) (2023)
- [Fast characterization of inducible regions of atrial fibrillation models with multi-fidelity Gaussian process classification](https://mlsanity.com/paper/2112.08075/) (2021)
- [Geometry-aware Active Learning of Spatiotemporal Dynamic Systems](https://mlsanity.com/paper/2504.19012/) (2025)
- [Adjoint-aided inference of Gaussian process driven differential equations](https://mlsanity.com/paper/2202.04589/) (2022)
- [Residual Deep Gaussian Processes on Manifolds](https://mlsanity.com/paper/2411.00161/) (2024)
- [On power sum kernels on symmetric groups](https://mlsanity.com/paper/2211.05650/) (2022)
- [Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshes](https://mlsanity.com/paper/2605.19305/) (2026)

## Abstract (arXiv)

In patients with atrial fibrillation, local activation time (LAT) maps are routinely used for characterising patient pathophysiology. The gradient of LAT maps can be used to calculate conduction velocity (CV), which directly relates to material conductivity and may provide an important measure of atrial substrate properties. Including uncertainty in CV calculations would help with interpreting the reliability of these measurements. Here, we build upon a recent insight into reduced-rank Gaussian processes (GP) to perform probabilistic interpolation of uncertain LAT directly on human atrial manifolds. Our Gaussian Process Manifold Interpolation (GPMI) method accounts for the topology of the atria, and allows for calculation of statistics for predicted CV. We demonstrate our method on two clinical cases, and perform validation against a simulated ground truth. CV uncertainty depends on data density, wave propagation direction, and CV magnitude. GPMI is suitable for probabilistic interpolation of other uncertain quantities on non-Euclidean manifolds.