Valeria V. Krzhizhanovskaya

Dongwei Ye, Valeria Krzhizhanovskaya, Alfons G. Hoekstra

Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations. However, the snapshots of the method require to be collected from the same discretisation, which is a straightforward process for physical parameters, but becomes challenging for geometrical problems, especially for those domains featuring unparameterised and unique shapes, e.g. patient-specific geometries. In this work, a data-driven surrogate model is proposed for the efficient prediction of blood flow simulations on similar but distinct domains. The proposed surrogate model leverages group surface registration to parameterise those shapes and formulates corresponding hemodynamics information into geometry-informed snapshots by the diffeomorphisms constructed between a reference domain and original domains. A non-intrusive reduced-order model for geometrical parameters is subsequently constructed using proper orthogonal decomposition, and a radial basis function interpolator is trained for predicting the reduced coefficients of the reduced-order model based on compressed geometrical parameters of the shape. Two examples of blood flowing through a stenosis and a bifurcation are presented and analysed. The proposed surrogate model demonstrates its accuracy and efficiency in hemodynamics prediction and shows its potential application toward real-time simulation or uncertainty quantification for complex patient-specific scenarios.

Khang Ly, Yury Kashnitsky, Savvas Chamezopoulos et al.

Classifying research output into context-specific label taxonomies is a challenging and relevant downstream task, given the volume of existing and newly published articles. We propose a method to enhance the performance of article classification by enriching simple Graph Neural Network (GNN) pipelines with multi-graph representations that simultaneously encode multiple signals of article relatedness, e.g. references, co-authorship, shared publication source, shared subject headings, as distinct edge types. Fully supervised transductive node classification experiments are conducted on the Open Graph Benchmark OGBN-arXiv dataset and the PubMed diabetes dataset, augmented with additional metadata from Microsoft Academic Graph and PubMed Central, respectively. The results demonstrate that multi-graphs consistently improve the performance of a variety of GNN models compared to the default graphs. When deployed with SOTA textual node embedding methods, the transformed multi-graphs enable simple and shallow 2-layer GNN pipelines to achieve results on par with more complex architectures.

Dongwei Ye, Pavel Zun, Valeria Krzhizhanovskaya et al.

In-Stent Restenosis is a recurrence of coronary artery narrowing due to vascular injury caused by balloon dilation and stent placement. It may lead to the relapse of angina symptoms or to an acute coronary syndrome. An uncertainty quantification of a model for In-Stent Restenosis with four uncertain parameters (endothelium regeneration time, the threshold strain for smooth muscle cells bond breaking, blood flow velocity and the percentage of fenestration in the internal elastic lamina) is presented. Two quantities of interest were studied, namely the average cross-sectional area and the maximum relative area loss in a vessel. Due to the computational intensity of the model and the number of evaluations required in the uncertainty quantification, a surrogate model, based on Gaussian process regression with proper orthogonal decomposition, was developed which subsequently replaced the original In-Stent Restenosis model in the uncertainty quantification. A detailed analysis of the uncertainty propagation and sensitivity analysis is presented. Around 11% and 16% of uncertainty are observed on the average cross-sectional area and maximum relative area loss respectively, and the uncertainty estimates show that a higher fenestration mainly determines uncertainty in the neointimal growth at the initial stage of the process. On the other hand, the uncertainty in blood flow velocity and endothelium regeneration time mainly determine the uncertainty in the quantities of interest at the later, clinically relevant stages of the restenosis process. The uncertainty in the threshold strain is relatively small compared to the other uncertain parameters.

Tesfamariam M. Abuhay, Sergey V. Kovalchuk, Klavdiya O. Bochenina et al.

This paper presents results of topic modeling and network models of topics using the International Conference on Computational Science corpus, which contains domain-specific (computational science) papers over sixteen years (a total of 5695 papers). We discuss topical structures of International Conference on Computational Science, how these topics evolve over time in response to the topicality of various problems, technologies and methods, and how all these topics relate to one another. This analysis illustrates multidisciplinary research and collaborations among scientific communities, by constructing static and dynamic networks from the topic modeling results and the keywords of authors. The results of this study give insights about the past and future trends of core discussion topics in computational science. We used the Non-negative Matrix Factorization topic modeling algorithm to discover topics and labeled and grouped results hierarchically.

C. D. Erdbrink, V. V. Krzhizhanovskaya, P. M. A. Sloot

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration methods. The coefficients are reverse engineered based on samples from a target function and its derivative used for training. The Runge-Kutta schemes are trained using the order condition equations. An appealing feature of the evolutionary method is the low number of model parameters. The population size, termination criterion and number of training points are determined in a sensitivity analysis. Computational results show good agreement between evolved and analytical coefficients. In particular, a new fifth-order Runge-Kutta scheme is computed which adheres to the order conditions with a sum of absolute errors of order 10^-14. Execution of the evolved schemes proved the intended orders of accuracy. The outcome of this study is valuable for future developments in the design of complex numerical methods that are out of reach by conventional means.