#### Student workshop on scientific computing 2023

May 25 - 28, 2023. Děčín, Czech Rep. + Online

Departments of Software Engineering and Mathematics
FNSPE CTU in Prague, Czech Republic

### List of abstracts

Numerical solution of the adjoint equation for the phase-field model
###### Michal Bohatý
FNSPE, CTU in Prague

Abstract:

This contribution is concerned with the optimization problem of controlling crystal growth by manipulating temperature at the edges of the crystallization region. Our approach is based on solving the adjoint equation, which enables efficient computation of gradient of the objective function. To describe phase transitions, we utilize the phase-field model consisting of partial differential equations. During the optimization process, those equations are solved numerically using the finite difference method. The main result of this work is a computational study in which we try to gain more insight into the problem of controlling crystallization using boundary conditions.

Optimal shape design of walls of blood flow mathematical model focusing on the total cavopulmonary connection
###### Jan Bureš
FNSPE, CTU in Prague

Abstract: This work deals with the optimization of shape of walls and with flow modelling of incompressible Newtonian fluid with a focus on modelling of blood flow in blood vessels. An optimization framework is presented and implemented, which can then be used to solve optimization problems involving fluid flow around rigid objects in 2D. The lattice Boltzmann method is used as the numerical solver and is briefly described. The theoretical section then describes the mathematical optimization methods used in this work. Interpolation boundary conditions, which are described and later used, are prescribed on the boundary of the objects. Thanks to the interpolation boundary conditions, the actual shape of the boundary of the objects is taken into account. Furthermore, the package used to automatically generate geometries used in the numerical simulations, which was implemented for the purpose of this work, is described. The next part demonstrates and analyses the application of the optimization framework on a series of test problems. Finally, the results of the optimization problem of a simplified 2D total cavopulmonary connection model are presented, which are in agreement with the available literature. Thus, the application of the optimization framework can be considered successful.

Simulation of airflow in an air quality measurement chamber
AGH University of Science and Technology

Abstract:

With the development of industry and technology, there is a growing need to study the quality of the air we breathe, which is a more complicated task than one might think. Measurement devices can behave very differently on different operating conditions. The quality of measurement can be affected by temperature, pressure, air humidity, level of measured parameter, air speed and air flow character.

The project involved the simulation of airflow in a measurement chamber used to measure concentration of PM2.5 particulate matter. For this purpose, a program implementing the Lattice Boltzmann Method on the D3Q27 lattice and cumulant based kernel was written.

Analysis of the results shows two vortices inside the chamber. This information can be used to design the geometry of new chamber versions which get rid of these vortices. It might lead to improved chamber measurement quality.

Non-Newtonian Blood Flow in Aortic Phantom: An Experimental and Computational Study
FNSPE, CTU in Prague, IKEM, Prague; Department of Pediatrics, Division of Pediatric Cardiology, UT Southwestern Medical Center, 5323 Harry Hines Blvd., Dallas, TX 75390, USA

Abstract:

This study investigates the need for non-Newtonian models to accurately represent blood flow in large vessels. A specially-designed phantom of the aorta is used in conjunction with phase-contrast magnetic resonance imaging (PC-MRI) and lattice Boltzmann method (LBM) computational fluid dynamics (CFD) simulations to compare the results of non-Newtonian and Newtonian fluid models. The experiments are conducted using three types of acrylic plates to represent varying degrees of aortic stenosis, and two constant flow rates. The PC-MRI flow measurements are assessed for accuracy, and it is found that they underestimate flow due to turbulence. The results show that, for the studied conditions, Newtonian models produce comparable results to non-Newtonian models, which suggests that they may be a more cost-effective alternative.

Comparison of Pre-Trained CNN in Image Classification
###### Kryštof Filip, Dana Majerová
FNSPE, CTU in Prague

Abstract:

In recent years, convolutional neural networks have become increasingly popular in various fields, and pre-trained models have shown promising results in image classification tasks. This contribution compares the performance of four pre-trained convolutional neural networks (Googlenet, Alexnet, Squeezenet, and Resnet-50) in distinguishing between different car species. Thousands of images were obtained from various sources using different web scraping techniques, including Google images, Bing images, Pinterest, second-hand and advertising sites. Our empirical results show that certain pre-trained models outperform others in this specific classification task. This presentation will provide complete results and further details on the methodology.

Oscilations of Absolute Moments of Fractal Diffusion Simulations
###### František Gašpar, Jaromír Kukal
FNSPE, CTU in Prague

Abstract:

This contribution addresses the discrepancy between analytical studies and published simulations regarding the presence of oscillations in fractal diffusion. By summarizing findings from multiple self-similar sets simulations, this contribution discusses oscillations in estimated absolute moments. The importance of incorporating oscillations into the dimension estimation procedure is emphasized, and a simple parametric form for the absolute moment model is proposed based on observed oscillatory behaviour.

Numerical model of non-isothermal flow around obstacles based on the lattice Boltzmann method
###### Dominik Horák
FNSPE, CTU in Prague

Abstract:

The work deals with the mathematical modeling of non-isothermal flow of incompressible Newtonian fluids. The aim of the work is to implement and describe heat transfer in a 3D numerical model. In the theoretical part, the mathematical model of non-isothermal flow of Newtonian fluids is presented together with a basic description of the cooling circuit of a student formula car. In the second part, the reader is introduced to the lattice Boltzmann method (LBM), and the last part discusses the results of the application of LBM with implemented heat transfer to the mathematical model. The implementation of heat transfer was successful, and the method produces satisfactory results.

Mathematical modeling of contrast agent transport in vascular bed with transfer to surrounding tissue in myocardial perfusion problems
###### Lenka Horvátová
FNSPE, CTU in Prague

Abstract: This work deals with mathematical modeling of problems arising during myocardial perfusion using the contrast agent. The description of the transport and transfer of the contrast agent from vascular bed to extravascular medium is divided into two tasks. First, the velocity in the vascular system is computed based on pressures. Then, a contrast agent with a given concentration is injected into the vascular system. The transfer of the contrast agent from the vascular system to the extravascular system is modeled using convolution with the Dirac delta function. In the second step, the concentration in both media is calculated. For this mathematical model, we consider an incompressible Newtonian fluid that is not subject to any external forces. The extravascular environment is considered to be porous and rigid. The main goal of this project is to solve the problem of transport and transfer of contrast agent in the vascular system using the finite volume method, and in the extravascular medium using the finite difference method.

Imperfect Classifier Using Hidden Classes
FNSPE, CTU in Prague

Abstract:

The presented imperfect classifier builds on using results of various learning methods, whether in the form of supervised or unsupervised learning. The results form so-called hidden classes. The number of these hidden classes is higher compared to the original output classes. The classifier stands on the optimal unioning of these hidden classes. The first two layers of the proposed classifier are for optional linear and or non-linear transformations. After this optional transformation, the set of imperfect classifiers is followed by hidden and final classification. The aim of the new classifier is to achieve the highest critical sensitivity.

Highly Efficient Phase Split Calculations in 2, 3, and 4 Phases through Combination of Stability, Minimization, and Newton Methods
###### Martin Jex, Jiří Mikyška, Abbas Firoozabadi
FNSPE, CTU in Prague, Chemical and Environmental Engineering,Yale University

Abstract:

Successful large-scale compositional reservoir simulation requires robust and efficient phase equilibrium calculations. In recent years a large number of papers have been published on the topic of three-phase vapor-liquid-aqueous (VLA) equilibria which frequently appear in hydrocarbon reservoirs. The presence of the aqueous phase increases the probability of equilibrium calculations to have issues. One may experience convergence problems or even not being able to distinguish a fourth phase altogether. This is generally due to the lack of good initial guesses, which is usually solved by proposing supplementary inital guesses which are designed to deal with a particular mixture. The commonly used approach is to perfrom a stability test before the equilibrium calculation, which determines whether it is needed to add an additional phase. Another benefit of this approach is that the result from the stability testing provides a good initial guess for the phase equilibrium calculation. In this contribution we present a robust algorithm which can deal with up to four phase equilibrium calculation. We demonstrate the algorithm and its robustness and efficiency in several examples from literature.

Overview of parallel and asynchronous computing in Python
FNSPE, CTU in Prague

Abstract: In recent years, Python has been consistently ranked as one of the most popular programming languages in the world. It is a general and high-level language that is used in many fields, including graphical interfaces, web applications, and data science. In this talk, we review its capabilities for for parallel and asynchronous computing, including coroutines with async and await syntax that was introduced in Python 3.5.

An Overview of 4D Flow Reconstruction using the Adjoint Method
###### Jan Kovář, Pavel Eichler, Kateřina Škardová
FNSPE, CTU in Prague, FNSPE CTU in Prague

Abstract: TBA

Optimization methods based on lattice Boltzmann method
###### Bořivoj Kronowetter
FNSPE, CTU in Prague

Abstract:

The aim of this work is to derive a method for the reconstruction of blood flow according to

data obtained from magnetic resonance imaging. As a first step, a simplified problem is solved, in which

the blood flow is simulated using the lattice Boltzmann method and the data from this simulation are

saved. We then try to reconstruct the control parameters from the stored data using the adjoint method.
Several optimization problems are going to be introduced. The acceleration caused by the external force field and the inlet velocity profile were chosen as the control parameters in these problems. Both the discrete adjoint approach and the continuous adjoint approach are going to be presented.
In the last part, numerical results of these approaches are compared.

Trajectory Surfaces of Framed Curvature Flow
###### Jiří Minarčík, Michal Beneš
FNSPE, CTU in Prague, FNSPE, CTU in Prague

Abstract: The framed curvature flow is a generalization of the curve shortening flow and the vortex filament equation, where the magnitude of the velocity vector is determined by the curvature, and its direction is given by an associated time-dependent moving frame. The flow can be defined in such a way that it sweeps out trajectory surfaces of constant mean or Gaussian curvature.

Visualization of curvature flow of smooth parametrized closed curves.
###### Maneesh Narayanan, Michal Beneš
FNSPE, CTU in Prague

Abstract:

This work consists of the motion of the closed curve given by the motion law \$V=K_{\Gamma}+F\$ (1). We used discretization techniques to solve (1) for various smooth parametrized closed curves. We studied the effects of \$K_{\Gamma}\$ and \$F\$ on the evolution of different types of smooth closed curves using MATLAB. Our aim of this work is to apply those techniques to physical science problems.

Brief Introdiction to VR-1 Reactor Technology and Reactor Kinetics
###### Sebastian Nývlt, Pavel Strachota, Aleš Wodecki
FNSPE, CTU in Prague

Abstract: This presentation should provide the mainly mathematical audience with the physical background for the previous presentation "Numerically Efficient Determination of Kinetic Parameters of the VR-1 Nuclear Reactor based on Experimental Data and ODE-Constrained Optimization" by Dr. Pavel Strachota. This short presentation will provide the audience with a summary of the key information from reactor physics of zero-power research reactors. The main goal is to summarize the theory of reactor kinetics and all possible approaches to determining the kinetic parameters of a research reactor. The presentation also briefly introduces the VR-1 reactor operated by the Dept. of Nuclear Reactors of FNSPE CTU in Prague where the results of this research might be implemented once the work is done and the approach is defended against the national regulatory body.

Phase field models in materials science and their numerical solution
###### Jan Palán
FNSPE, CTU in Prague

Abstract: This thesis deals with the simulation of crystal growth during solidification of a pure supercooled substance using the phase field method, which describes the phase interface as a smooth transition layer between the liquid and solid state. Firstly, the mathematical model is presented. The anisotropic model for pure substance in the three-dimensional case is based on Finsler geometry. Furthermore, the work summarizes the phase field approaches to modeling binary alloy soldification. The main objective is the numerical solution of the phase field models on unstructured meshes. Due to the easy adaptation to an unstructured mesh, the finite volume method is used to discretize models. The implementation of the program in C++ is based on the GTMesh library. Finally, numerical simulations are performed especially to compare the phase field model behavior on an unstructured mesh and on a structured one.

Pore-network modeling of air entrapment in randomized pore medium
###### Tomáš Princ, Michal Sněhota
FCE, CTU in Prague, FCE, CTU in Prague

Abstract:

The research deals with pore-network (PN) modeling and its use for the simulation of flow in the pore medium. This model allows the simulation of water flow on the pore scale, thanks to which it is possible to  relatively accurately capture the process of air entrapment. Furthermore, a solution for two-phase flow is used, which makes it possible to determine the relative hydraulic conductivity values dependent on the air saturation.

Geometric image processing by the Allen-Cahn equation
###### Aaron Schick
FNSPE, CTU in Prague

Abstract: This work examines the use of PDEs for image processing, specifically the Allen-Cahn equation and its modification on rectangular domains. Differential law of motion of curves according to its curvature is introduced and we discuss its connection to the solution of the Allen-Cahn equation. We present a segmentation model based on this observation and apply it to test cardiac MRI data.

Aplication of fuzzy management to analysis financial state of firms
###### Adam Štampach, doc. Ing. Quang Van Tran, Ph.D.
FNSPE, CTU in Prague

Abstract:

Thesis examines the possibility of applying fuzzy management in financial analysis, specifically the prediction of corporate bankruptcy according to selected financial indicators. This task was implemented by converting Altman’s bankruptcy model into a fuzzy form, and subsequently its use was verified using a data file of approximately 10 500 companies. The prediction results of the proposed fuzzy model were compared with the results obtained by other selected bankruptcy models on a data set of approximately 5 500 companies.

Physics-informed DeepONets for HJB equation arising from portfolio management
###### Cyril Izuchukwu Udeani, Daniel Sevcovic
Comenius University in Bratislava, Comenius University in Bratislava

Abstract:

Several differential equations from many scientific and engineering fields for modeling physical phenomena are analytically intractable, especially in high-dimensional space. Traditional numerical methods, including neural network approaches, have been extensively used to approximate solutions of such differential equations. Although some machine learning approaches, such as physics-informed neural networks, are faster than the conventional numerical methods; however, a slight change in the underlying parameters governing the differential equation could result in the retraining of the model. Therefore, in this study, we employ the physics-informed DeepONet (PI-DeepONet) to approximate the solution operator of a fully nonlinear partial differential equation arising from finance. PI-DeepONet incorporates known physics into the neural network, which consists of a deep neural network that learns the solution of the PDE and an operator network that enforces the PDE at each iteration. We consider a fully nonlinear Hamilton--Jacobi--Bellman (HJB) equation arising from the stochastic optimization problem, where the goal of an investor is to maximize the conditional expected value of the terminal utility of a portfolio. The fully nonlinear HJB equation is first transformed into a quasilinear parabolic equation using the Ricatti transform. Then, the solution of the transformed quasilinear equation is approximated using PI-DeepONet.

High-throughput readout and filtering systems for the AMBER experiment
###### Martin Zemko
FNSPE, CTU in Prague

Abstract:

Traditional triggered data acquisition systems provide limited capabilities of acquisition modes, usually relying on perfectly synchronized detectors. This contribution describes a novel triggerless approach removing low-level trigger logic and detector dead times. We developed such a streaming acquisition system for the AMBER experiment at CERN. It is based on high-speed data handling FPGA modules and advanced software processing on conventional x86 processors. The triggerless mode provides enough time for complex data filtering and online track reconstruction. Moreover, the readout system utilizes a custom data protocol optimized for the needs of the streaming system. The filtering procedure takes place in a distributed server farm playing the role of the high-level filter. For this purpose, we implemented a high-performance filtering framework providing high-throughput, parallel algorithms and load balancing to cope with excessive data rates. Furthermore, this work also describes the filtering pipeline and the generator chain simulating the readout system and producing artificial data for system validation.

Dynamics of Signal Propagation in Excitable Media
###### Dominik Žurek
FNSPE, CTU in Prague

Abstract: The contribution is devoted to mathematical modelling of signal propagation in excitable media by the FitzHugh–Nagumo model. This model weakly formulated, analyzed and numerically solved in 1D and 2D. It is also converted to curvilinear coordinates along a closed curve simulating the myocard crossection. Numerical solution is obtained by the finite-difference method and method of lines and verified by evaluating the experimental order of convergence.