# Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networks

arXiv: https://arxiv.org/abs/2503.17402 · HTML: https://mlsanity.com/paper/2503.17402/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 64 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 30 of 31)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [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)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [Long-time integration of parametric evolution equations with physics-informed DeepONets](https://mlsanity.com/paper/2106.05384/) (2021)
- [Improved architectures and training algorithms for deep operator networks](https://mlsanity.com/paper/2110.01654/) (2021)
- [Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling](https://mlsanity.com/paper/2207.02338/) (2022)
- [NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework](https://mlsanity.com/paper/2012.07938/) (2020)
- [Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads](https://mlsanity.com/paper/2306.08218/) (2023)
- [Parameterized Physics-informed Neural Networks for Parameterized PDEs](https://mlsanity.com/paper/2408.09446/) (2024)
- [Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network](https://mlsanity.com/paper/2108.11985/) (2021)
- [Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations](https://mlsanity.com/paper/2212.04663/) (2022)
- [4DFlowNet: Super-Resolution 4D Flow MRI using Deep Learning and Computational Fluid Dynamics](https://mlsanity.com/paper/2004.07035/) (2020)
- [Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning](https://mlsanity.com/paper/2407.15887/) (2024)
- [Random Weight Factorization Improves the Training of Continuous Neural Representations](https://mlsanity.com/paper/2210.01274/) (2022)
- [A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel construction](https://mlsanity.com/paper/2310.00057/) (2023)
- [Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI](https://mlsanity.com/paper/2302.12835/) (2023)
- [Predictions of Transient Vector Solution Fields with Sequential Deep Operator Network](https://mlsanity.com/paper/2311.11500/) (2023)
- [Physics-constrained DeepONet for Surrogate CFD models: a curved backward-facing step case](https://mlsanity.com/paper/2503.11196/) (2025)
- [A data-driven Reduced Order Method for parametric optimal blood flow control: application to coronary bypass graft](https://mlsanity.com/paper/2206.15384/) (2022)

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

- [Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets](https://mlsanity.com/paper/2608.13629/) (2026)
- [Physics Informed Neural Network model for the dynamical study of Abdominal Aortic Aneurysm](https://mlsanity.com/paper/2609.15104/) (2026)
- [Reconstruction of 4D Mitral Regurgitation Hemodynamics from Sparse Planar Data using Deep Operator Networks with Test-Time Adaptation](https://mlsanity.com/paper/2609.20857/) (2026)

## Abstract (arXiv)

Due to the limited accuracy of 4D Magnetic Resonance Imaging (MRI) in identifying hemodynamics in cardiovascular diseases, the challenges in obtaining patient-specific flow boundary conditions, and the computationally demanding and time-consuming nature of Computational Fluid Dynamics (CFD) simulations, it is crucial to explore new data assimilation algorithms that offer possible alternatives to these limitations. In the present work, we study Physics-Informed Neural Networks (PINNs), Deep Operator Networks (DeepONets), and their Physics-Informed extensions (PI-DeepONets) in predicting vascular flow simulations in the context of a 3D Abdominal Aortic Aneurysm (AAA) idealized model. PINN is a technique that combines deep neural networks with the fundamental principles of physics, incorporating the physics laws, which are given as partial differential equations, directly into loss functions used during the training process. On the other hand, DeepONet is designed to learn nonlinear operators from data and is particularly useful in studying parametric partial differential equations (PDEs), e.g., families of PDEs with different source terms, boundary conditions, or initial conditions. Here, we adapt the approaches to address the particular use case of AAA by integrating the 3D Navier-Stokes equations (NSE) as the physical laws governing fluid dynamics. In addition, we follow best practices to enhance the capabilities of the models by effectively capturing the underlying physics of the problem under study. The advantages and limitations of each approach are highlighted through a series of relevant application cases. We validate our results by comparing them with CFD simulations for benchmark datasets, demonstrating good agreements and emphasizing those cases where improvements in computational efficiency are observed.