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

TL;DR

The paper tackles the challenge of efficiently predicting patient-specific vascular flow in abdominal aortic aneurysms by comparing Physics-Informed Neural Networks (PINNs), Deep Operator Networks (DeepONets), and their Physics-Informed variants (PI-DeepONets). It formulates an idealized 3D AAA problem governed by the Navier–Stokes equations and develops a comprehensive data-prep and training framework that leverages CFD ground truth and region-specific losses. The key contributions include a side-by-side assessment of PINN and (PI-)DeepONet approaches in a 3D AAA setting, enhanced training strategies (non-dimensionalization, Fourier features, Grad Norm, RWF, Modified-MLP), and a multi-input/multi-output DeepONet architecture enabling rapid, physics-consistent surrogate predictions with substantial speedups over CFD. The results show that PINNs can work robustly with sparse or noisy data, while (PI-)DeepONet provides faster inference and good accuracy across varied boundary conditions, offering a practical route toward real-time vascular flow analysis in clinical contexts.

Abstract

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.

Figures (11)

• Figure 1: Illustrative example of the PINNs training process.
• Figure 2: DeepONet workflow.
• Figure 3: Abdominal Aortic Aneurysm geometry.
• Figure 4: Schematic representation of a $V$-dependent stratified dataset.
• Figure 5: Schematic representation of the dataset splitting process.