# On the accuracy of implicit neural representations for cardiovascular anatomies and hemodynamic fields

arXiv: https://arxiv.org/abs/2510.20970 · HTML: https://mlsanity.com/paper/2510.20970/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 85 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Real-time Neural Radiance Caching for Path Tracing](https://mlsanity.com/paper/2106.12372/) (2021)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [Spatial Functa: Scaling Functa to ImageNet Classification and Generation](https://mlsanity.com/paper/2302.03130/) (2023)
- [NeurAR: Neural Uncertainty for Autonomous 3D Reconstruction with Implicit Neural Representations](https://mlsanity.com/paper/2207.10985/) (2022)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [Mitigating spectral bias for the multiscale operator learning](https://mlsanity.com/paper/2210.10890/) (2022)
- [A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems](https://mlsanity.com/paper/1909.11759/) (2019)

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

- [FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions](https://mlsanity.com/paper/2603.19331/) (2026)

## Abstract (arXiv)

Implicit neural representations (INRs, also known as neural fields) have recently emerged as a powerful framework for knowledge representation, synthesis, and compression. By encoding fields as continuous functions within the weights and biases of deep neural networks-rather than relying on voxel- or mesh-based structured or unstructured representations-INRs offer both resolution independence and high memory efficiency. However, their accuracy in domain-specific applications remains insufficiently understood. In this work, we assess the performance of state-of-the-art INRs for compressing hemodynamic fields derived from numerical simulations and for representing cardiovascular anatomies via signed distance functions. We investigate several strategies to mitigate spectral bias, including specialized activation functions, both fixed and trainable positional encoding, and linear combinations of nonlinear kernels. On realistic, space- and time-varying hemodynamic fields in the thoracic aorta, INRs achieved remarkable compression ratios of up to approximately 230, with maximum absolute errors of 1 mmHg for pressure and 5-10 cm/s for velocity, without extensive hyperparameter tuning. Across 48 thoracic aortic anatomies, the average and maximum absolute anatomical discrepancies were below 0.5 mm and 1.6 mm, respectively. Overall, the SIREN, MFN-Gabor, and MHE architectures demonstrated the best performance. Source code and data is available at https://github.com/desResLab/nrf.