# Localized FNO for Spatiotemporal Hemodynamic Upsampling in Aneurysm MRI

arXiv: https://arxiv.org/abs/2507.13789 · HTML: https://mlsanity.com/paper/2507.13789/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 15 of 15)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling](https://mlsanity.com/paper/2203.08205/) (2022)
- [Super-Resolution Neural Operator](https://mlsanity.com/paper/2303.02584/) (2023)
- [Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics](https://mlsanity.com/paper/2205.03990/) (2022)
- [Domain Agnostic Fourier Neural Operators](https://mlsanity.com/paper/2305.00478/) (2023)
- [Canonical normalizing flows for manifold learning](https://mlsanity.com/paper/2310.12743/) (2023)
- [Explicit and data-Efficient Encoding via Gradient Flow](https://mlsanity.com/paper/2412.00864/) (2024)
- [Energy-Based Prior Latent Space Diffusion model for Reconstruction of Lumbar Vertebrae from Thick Slice MRI](https://mlsanity.com/paper/2412.00511/) (2024)

## Built on by (most cited first, 2 of 2)

- [Operator Flow Matching for Timeseries Forecasting](https://mlsanity.com/paper/2510.15101/) (2025)
- [Parameter-Efficient Adaptation of Pretrained Language Models for Time-Series Forecasting](https://mlsanity.com/paper/2609.15344/) (2026)

## Abstract (arXiv)

Hemodynamic analysis is essential for predicting aneurysm rupture and guiding treatment. While magnetic resonance flow imaging enables time-resolved volumetric blood velocity measurements, its low spatiotemporal resolution and signal-to-noise ratio limit its diagnostic utility. To address this, we propose the Localized Fourier Neural Operator (LoFNO), a novel 3D architecture that enhances both spatial and temporal resolution with the ability to predict wall shear stress (WSS) directly from clinical imaging data. LoFNO integrates Laplacian eigenvectors as geometric priors for improved structural awareness on irregular, unseen geometries and employs an Enhanced Deep Super-Resolution Network (EDSR) layer for robust upsampling. By combining geometric priors with neural operator frameworks, LoFNO de-noises and spatiotemporally upsamples flow data, achieving superior velocity and WSS predictions compared to interpolation and alternative deep learning methods, enabling more precise cerebrovascular diagnostics.