Combined Parameter and Model Reduction of Cardiovascular Problems by Means of Active Subspaces and POD-Galerkin Methods

Reconstruction of blood flow velocity with deep learning information fusion from spectral ct projections and vessel geometry

In this work, we investigate a new deep learning reconstruction method of blood flow velocity within deformed vessels from contrast enhanced X-ray projections and vessel geometry. The principle of the method is to perform linear or nonlinear dimension reductions on the Radon projections and on the mesh of the vessel. These low dimensional projections are then fused to obtain the velocity field in the vessel. The accuracy of the reconstruction method is proved using various neural network architectures with realistic unsteady blood flows. The approach leverages the vessel geometry information and outperforms the simple PCA-net.

Reduced order modelling of intracranial aneurysm flow using proper orthogonal decomposition and neural networks

Reduced order modelling (ROMs) methods, such as proper orthogonal decomposition (POD), systematically reduce the dimensionality of high-fidelity computational models and potentially achieve large gains in execution speed. Machine learning (ML) using neural networks has been used to overcome limitations of traditional ROM techniques when applied to nonlinear problems, which has led to the recent development of reduced order models augmented by machine learning (ML-ROMs). However, the performance of ML-ROMs is yet to be widely evaluated in realistic applications and questions remain regarding the optimal design of ML-ROMs. In this study, we investigate the application of a non-intrusive parametric ML-ROM to a nonlinear, time-dependent fluid dynamics problem in a complex 3D geometry. We construct the ML-ROM using POD for dimensionality reduction and neural networks for interpolation of the ROM coefficients. We compare three different network designs in terms of approximation accuracy and performance. We test our ML-ROM on a flow problem in intracranial aneurysms, where flow variability effects are important when evaluating rupture risk and simulating treatment outcomes. The best-performing network design in our comparison used a two-stage POD reduction, a technique rarely used in previous studies. The best-performing ROM achieved mean test accuracies of 98.6% and 97.6% in the parent vessel and the aneurysm, respectively, while providing speed-up factors of the order10 5 .

Accelerated simulation methodologies for computational vascular flow modelling

Vascular flow modelling can improve our understanding of vascular pathologies and aid in developing safe and effective medical devices. Vascular flow models typically involve solving the nonlinear Navier-Stokes equations in complex anatomies and using physiological boundary conditions, often presenting a multi-physics and multi-scale computational problem to be solved. This leads to highly complex and expensive models that require excessive computational time. This review explores accelerated simulation methodologies, specifically focusing on computational vascular flow modelling. We review reduced order modelling (ROM) techniques like zero-/one-dimensional and modal decomposition-based ROMs and machine learning (ML) methods including ML-augmented ROMs, ML-based ROMs and physics-informed ML models. We discuss the applicability of each method to vascular flow acceleration and the effectiveness of the method in addressing domain-specific challenges. When available, we provide statistics on accuracy and speed-up factors for various applications related to vascular flow simulation acceleration. Our findings indicate that each type of model has strengths and limitations depending on the context. To accelerate real-world vascular flow problems, we propose future research on developing multi-scale acceleration methods capable of handling the significant geometric variability inherent to such problems.

Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method

Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular, we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions. The implementation is thoroughly discussed and tested on more challenging benchmarks than the ones already present in the literature, for which dimension reduction with active subspaces produces already good results. Finally, we show a whole pipeline for the design of response surfaces with the new methodology in the context of a parametric computational fluid dynamics application solved with the discontinuous Galerkin method.

Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation

Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.

Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes and to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.