Pavel Eichler

Abstract:

This contribution introduces you to the basics of quantum computing problematics. In this context, one of the currently investigated problems is the preparation of the initial state of quantum qubit and accurate operation with its states. Instead of amazing new results, open questions will be discussed and our plans for the future will be presented. Finally, you can look forward to LBM in a quantum context as well.

František Hájek, Filip Dominec

Abstract:

Semiconductor research produce large amount of data which need further processing by numerical methods. Once evaluated, these large datasets can serve also as a potential input for machine learning processes aiming to speed up the development of desired semiconductor devices. In this talk, I would like to provide an overview of topics involving numerical modelling which have been dealt with in the past years at Department of Semiconductors, Institute of Physics, CAS. The research has been focused on development of nitride-based scintillators for fast-timing application. Outcomes of the experimental characterization of these devices often need a numerical processing like image recognition, image overlay methods or filtering and fitting of spectral maps.  Approaches to these tasks will be introduced.

Machine learning algorithms were also used to design device with optimal performance and the results will be shown.

Vladimír Jarý, Martin Zemko, Jan Vondruška, Jozef Hrdý

Abstract:

Nowadays, the modern experiments in the particle physics heavily rely on the efficient data acquisition systems (DAQ). In this contribution we will focus on the DAQ of the AMBER experiment at CERN laboratory. At first, we will briefly introduce the scientific program of the experiment. Then we will describe the traditional architecture of the DAQ systems that strongly depend on the trigger subsystem that selects potential event candidates in high rate, distributed network environment almost in real time. We will analyze disadvantages of such systems which will lead us to proposal of the triggerless DAQ in which the filtering logic is moved to the higher levels (the high level trigger HLT). This allows development of more sophisticated filtering algorithms that in turn select more appropriate event candidates. We will discuss the design and current status of the implementation of this system in the context of the AMBER experiment. 

We conclude the contribution with presentation of plans of future upgrades of the system that include several opportunities for students of Bachelor's and Master's degree courses at out faculty.

Jakub Klinkovský

Abstract: Scientific visualization in our research group is mostly based on the traditional VTK file formats. However, these formats are not flexible and cause bottlenecks in high-performance applications operating on large datasets. In this talk, we summarize our progress towards using the ADIOS2 library, a unified, MPI-based and streaming-oriented high-performance I/O framework, for managing data output in the TNL-LBM project.

Miroslav Kolář

Abstract:

We discuss the motion of closed non-intersecting space curves driven by curvature in binormal and normal directions coupled with advection-diffusion equation for a scalar quantity defined on a curve. We formulate the general motion law in space in binormal and normal directions by curvature and mention some known analytical properties. The finite-volume scheme allows us to solve both the advection-diffusion problem defined on the curve as well as the motion of the curve itself. The numerical scheme is stabilized by the tangential velocity redistributing discretization nodes. We demonstrate the behavior of the solution on several computational studies combining the motion in normal and binormal velocity with the evolution of the scalar quantity.

Jaromír Kukal, Michal Beneš

Abstract:

One-dimensional partice hopping with constrained variance is a well known model of Brownian motion and therefore the traditional particle diffusion.  Model analysis is possible using the Central Limit Theorem (CLT) which produces Einstein formula. Another strategies of heavy tile hopping with discrete Pareto distribution can be studied by the Generalized CLT (GCLT).

Jakub Solovský, Aleš Wodecki, Monika Balázsová, Kateřina Škardová, Tomáš Oberhuber

Abstract:

The refractive index of thermo-optic materials changes significantly with temperature. This property allows for a layer of material with a certain temperature profile to act as a lens with desired optical properties. The goal is to find the heat fluxes through the domain boundary that result in the given temperature profile at the given time while considering heat losses into the surrounding material.

We solve the PDE-constrained optimization problem using the gradient descent method. For the computation of the objective function gradient, we employ the approach based on solving the adjoint equation for Lagrange multipliers.  Both the primary and adjoint problems are solved by the Mixed-Hybrid Finite Element Method with fully implicit discretization in time.

We demonstrate that the temperature profiles given by Zernike polynomials on a circular domain can be obtained.

Martin Srnec, Zuzanna Wojdyla, Jan Kovář, Radek Fučík

Abstract:

I will briefly introduce computational chemistry, a field that provides a unique perspective on the properties and reactivity of molecules. In my talk, I will then introduce some of our concepts and theoretical frameworks that aim to understand the physicochemical factors that determine the rate and selectivity of chemical reactions and enable reliable predictions.

Pavel Strachota

Abstract: We present a simple and flexible Discrete Element Method (DEM) model for simulating the dynamics of spherical particle systems. The aim is to utilize commonly available ODE integrators that are usually inappropriate for DEM, in particular the Runge-Kutta-Merson and Dormand-Prince solvers with adaptive time stepping. This is achieved by using a novel soft contact model with repulsive and frictional forces smoothly varying in time, which allows the time step adaptivity algorithms to work properly. The model parameters are calibrated so that a realistic random close packing can be obtained from simulations of particle settling at the bottom of a container. A reference minimal implementation in MATLAB and a complete implementation in C with OpenMP parallelization are introduced and their computational performance is assessed.

Robert Straka

Abstract:

The assessment of volumetric blood flow in bypass grafts stands as a pivotal parameter indicative of the overall success of surgical intervention. In cases where blood flux diminishes significantly, the efficacy of the bypass may be compromised, potentially leading to failure. We present a novel bypass graft simulation tool (currently under development :). This tool comprises three integral components: segmentation of X-ray coronary angiography, bypass graft planning, and simulation of blood flow, alongside an anastomosis optimization module. Our presentation deals primarily with the blood flow modeling aspect, which is performed by the Lattice Boltzmann Method. We conduct simulations on three scenarios involving the left coronary artery -- healthy, stenosed and stenosed with a bypass -- and verify our findings with those obtained from the SimVascular - a specialized software for medical image data segmentation and patient specific blood flow simulation and analysis.

Daniel Ševčovič, Cyril Udeani

Abstract:

In this talk we analyze solutions of a non-local nonlinear partial integro-differential equation (PIDE) in multidimensional spaces. Such class of PIDE often arises in financial modeling. We employ the theory of abstract semilinear parabolic equations in order to prove existence and uniqueness of solutions in the scale of Bessel potential spaces. We consider a wide class of Levy measures satisfying suitable growth conditions near the origin and infinity. The novelty consists in the generalization of already known results in the one space dimension to the multidimensional case. We consider Black-Scholes models for option pricing on underlying assets following a Levy stochastic process with jumps. As an application to option pricing in the one-dimensional space, we consider a general shift function arising from nonlinear option pricing models taking into account a large trader stock-trading strategy. We prove existence and uniqueness of a solution to the nonlinear PIDE in which the shift function may depend on a prescribed large investor stock-trading strategy function.

Quang Van Tran

Abstract:

We investigate which distribution is most appropriate for modeling returns of cryptocurrencies. We study distribution of both unconditional returns and conditional returns. Four well-known heavy-tailed  distributions Generalized Normal, Student t-, Normal Inverse Gausian, Alpha stable and two recently suggested distributions and four GARCH models plain GARCH, range GARCH, TGARCH and EGARCH are studied. The results estimated for Bitcoin, Binance Coin, Ethereum, Solana and Ripple are unambiguous. For each cryptocurrency, the most appropriate distribution is the generalized normal distribution. This conclusion holds not only for returns, but also for conditional returns (residuals from a conditional mean model in the presence of heteroscedasticity), and for all considered volatility models. The most suitable GARCH model is the EGARCH model, and the range GARCH model performs very well in some cases.

Cyril Izuchukwu Udeani, Daniel Sevcovic

Abstract: This study focuses on approximating the solution operator of a fully nonlinear partial differential equation arising from finance using machine learning techniques. 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 value function of the nonlinear HJB equation describes the optimal portfolio selection strategy. 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 deep learning. Our qualitative analysis shows that the solution operator of the associated HJB equation can effectively be learned using a deep learning approach.

Aleš Wodecki

Abstract: In certain applications, classical gradient based methods often fail to find local minima due to the cost functional or feasible sets being non-convex. There exist techniques, which may be applied in such circumstances with associated numerical treatments that lead to computational results. The benefits of such methods, as well as the challenges, are briefly outlined and discussed. In particular, we focus on introducing polynomial optimization as a robust method used to arrive at global minima, whose applications range from optimization over graphs to PDE constrained optimization.

Serhii Yaskovets

Abstract:

Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. OpenFPM is an open-source C++ framework that provides transparent and scalable infrastructure for shared-memory and distributed-memory implementations of particles-only and hybrid particle-mesh simulations of both discrete and continuous models. The infrastructure is complemented with frequently used numerical routines, as well as interfaces to state-of-the-art third-party numerical libraries. We present the architecture and design of OpenFPM, general overview of the underlying abstractions, and benchmark results in applications ranging from Smoothed-Particle Hydrodynamics (SPH) to Molecular Dynamics (MD), Discrete Element Methods (DEM), Vortex Methods, stencil codes (finite differences), and high-dimensional Monte Carlo sampling (CMA-ES).