Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator–regression neural network

Abstract

Aortic dissection progresses mainly via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasi-static pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection along the aorta can be affected by spatial distributions of structurally significant interlamellar struts that connect adjacent elastic lamellae. In particular, diverse histological microstructures may lead to differential mechanical behaviour during dissection, including the pressure–volume relationship of the injected fluid and the displacement field between adjacent lamellae. In this study, we develop a data-driven surrogate model of the delamination process for differential strut distributions using DeepONet, a new operator–regression neural network. This surrogate model is trained to predict the pressure–volume curve of the injected fluid and the damage progression within the wall given a spatial distribution of struts, with in silico data generated using a phase-field finite-element model. The results show that DeepONet can provide accurate predictions for diverse strut distributions, indicating that this composite branch-trunk neural network can effectively extract the underlying functional relationship between distinctive microstructures and their mechanical properties. More broadly, DeepONet can facilitate surrogate model-based analyses to quantify biological variability, improve inverse design and predict mechanical properties based on multi-modality experimental data.

MIONet: Learning multiple-input operators via tensor product

“…Several approaches of neural operators have been recently proposed such as deep operator network (DeepONet) [26,27,28] and Fourier neural operator (FNO) [20,28], graph kernel network [21,46], and others [33,1,41,36]. Among these approaches, DeepONet has been applied and demonstrated good performance in diverse applications, such as high-speed boundary layer problems [7], multiphysics and multiscale problems of hypersonics [31] and electroconvection [2], multiscale bubble growth dynamics [22,23], fractional derivative operators [27], stochastic differential equations [27], solar-thermal system [34], and aortic dissection [45]. Several extensions of DeepONet have also been developed, such as Bayesian DeepONet [24], DeepONet with proper orthogonal decomposition (POD-DeepONet) [28], multiscale DeepONet [25], neural operator with coupled attention [13], and physics-informed DeepONet [42,9].…”

Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems

“…In the last few years, a new family of machine learning model, deep neural operators, have been proposed to learn the solution operator of a PDE system implicitly [42,44,49,89]. Unlike another type of scientific machine learning, physics-informed neural networks (PINNs) [67], these neural operators can solve a PDE system given a new instance of interface conditions or model parameters without retraining [13,27,43,45,46,51,87]. Hence, such computational advantage enables neural operators to serve as an efficient surrogate model in multiscale coupling tasks, and especially for time-depenendent multiscale problems, which even today have remained prohibitively expensive.…”

Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport

“…DeepONet and its extensions have demonstrated good performance in diverse applications, such as fractional-derivative operators [12], stochastic differential equations [12], high-speed boundarylayer problems [29], multiscale bubble growth dynamics [30,31], solar-thermal systems [32], aortic dissection [33], multiphysics and multiscale problems of electroconvection [20] and hypersonics [21], power grids [23], and multiscale modeling of mechanics problems [34]. It has also been theoretically proved that DeepONet may break the curse of dimensionality in some PDEs [35,36,37].…”