# BP-DeepONet: A new method for cuffless blood pressure estimation using the physcis-informed DeepONet

arXiv: https://arxiv.org/abs/2402.18886 · HTML: https://mlsanity.com/paper/2402.18886/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 60 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Failure-informed adaptive sampling for PINNs](https://mlsanity.com/paper/2210.00279/) (2022)
- [PPG2ABP: Translating Photoplethysmogram (PPG) Signals to Arterial Blood Pressure (ABP) Waveforms using Fully Convolutional Neural Networks](https://mlsanity.com/paper/2005.01669/) (2020)
- [Generalization Error Analysis of Neural networks with Gradient Based Regularization](https://mlsanity.com/paper/2107.02797/) (2021)

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

- [Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networks](https://mlsanity.com/paper/2503.17402/) (2025)
- [HIPNO: Symmetry-Aware Physics-Informed Neural Operators for Noninvasive Hemodynamic Inference](https://mlsanity.com/paper/2608.10011/) (2026)

## Abstract (arXiv)

Cardiovascular diseases (CVDs) are the leading cause of death worldwide, with blood pressure serving as a crucial indicator. Arterial blood pressure (ABP) waveforms provide continuous pressure measurements throughout the cardiac cycle and offer valuable diagnostic insights. Consequently, there is a significant demand for non-invasive and cuff-less methods to measure ABP waveforms continuously. Accurate prediction of ABP waveforms can also improve the estimation of mean blood pressure, an essential cardiovascular health characteristic. This study proposes a novel framework based on the physics-informed DeepONet approach to predict ABP waveforms. Unlike previous methods, our approach requires the predicted ABP waveforms to satisfy the Navier-Stokes equation with a time-periodic condition and a Windkessel boundary condition. Notably, our framework is the first to predict ABP waveforms continuously, both with location and time, within the part of the artery that is being simulated. Furthermore, our method only requires ground truth data at the outlet boundary and can handle periodic conditions with varying periods. Incorporating the Windkessel boundary condition in our solution allows for generating natural physical reflection waves, which closely resemble measurements observed in real-world cases. Moreover, accurately estimating the hyper-parameters in the Navier-Stokes equation for our simulations poses a significant challenge. To overcome this obstacle, we introduce the concept of meta-learning, enabling the neural networks to learn these parameters during the training process.