Laskennallinen tekniikka ja teknillinen fysiikka - Computational Engineering

Functional analysis is a classical field of mathematics, which aims to describe general vector spaces (e.g. function spaces or graphs) and mappings defined on these spaces, and aims to characterize their relationships and properties. Functional analysis offers tools for deeper understanding of many mathematical phenomena such as Fourier transform or numerical analysis. The topic of functional analysis is contemporary, since the data masses studied in modern science are often vast and high-dimensional. It is necessary to understand how different mappings between such data sets scale as the size or the dimension of the data increases. The contents of this course are mostly theoretical and exercises emphasise being able to prove mathematical statements.

This is a research level course mainly intended to final year MSc students and PhD students. The exact content is always agreed with the students. Topics include, but are not limited to, connections between deep Gaussian processes, deep neural networks and stochastic differential equations; implementation needed sampling methods with MCMC, variational Bayes or optimisation as needed; mixture of Gaussian process experts; high-performance computing and random field models for Bayesian inversion.

Kurssilla ei käsitellä uusia menetelmiä vaan sovelletaan aiemmin opittuja lakennallisen tekniikan menetelmiä käytännön ongelmien ratkaisemiseen.

Characteristics and pre-processing of data, linear and nonlinear dimensionality reduction. Logistic, multivariate statistical methods and advanced extensions of the methods. Deep neural networks, semi-supervised learning and generative models. Case-based topics on data analysis and machine learning.

Partial differential equations in mathematical modeling Nonlinear conservation laws Wave equation Fluid mechanics and Navier-Stokes equations

- Integraalilaskenta usean muuttujan funktioilla.- Kaksinkertainen ja kolminkertainen integraali.- Koordinaatistomuunnoksia.- Skalaarikentän viivaintegraali.- Konservatiiviset vektorikentät.- Vektorikentän viivaintegraali.- Greenin lause.- Skalaarikentän pintaintegraali.- Vektorikentän pintaintegraali.- Gradientti, divergenssi ja roottori.- Gaussin lause.- Stokesin lause.- Vektoripotentiaali.- Ylläolevien numeerinen laskenta.

Our course has three main topics: Markov chain Monte Carlo methods, Gaussian process regression, Kalman filtering. As examples we will use parametric models for curve fitting and estimation of parameters and states of stochastic processes. In particular, we use the Ornstein-Uhlenbeck process as an example. We will focus on building statistical models using Bayesian methods, the use of appropriate methods (optimization, statistical methods) and practical coding. 

Kurssille kutsutaan puhumaan laskennalliselta tekniikalta lähiaikoina valmistuneita ja eri yrityksiin menneitä kertomaan esimerkiksi: - minkälaisia ongelmia he ratkovat, - minkälaisia ohjelmistoja he käyttävät, - mitä laskentaa he tekevät, - minkälaisilla koneilla tekevät laskentaa. - Lisäksi kurssiin liittyy esimerkiksi LUTin spinoff-firmojen esittelyä.

The Orientation Days activities. Practical study-related information, degree requirements. Planning of Master's studies. Preparation of the electronic personal study plan at the ePSP workshop. Getting familiar with the support in monitoring the progress of the studies. Use of digital services in studies. The Academic Library collections and databases. Information security training.

Perustiedot akateemisesta yksikköstä, koulutusohjelmasta ja yliopisto-opiskelusta. Opiskelija tekee henkilökohtaisen opiskelusuunnitelman omien tavoitteidensa mukaisesti. Opiskelija tutustuu yliopiston tiedekirjaston palveluihin ja tietoturvaan liittyviin seikkoihin. Opiskelija tutustuu matemaattisen tekstin tuotantoon Latex-ympäristössä.

Kirjallisen kandidaatintyön laatiminen ja sen suullinen esitys seminaarissa. Kandidaatintyön laatimisen yhteydessä käydään läpi tutkimuksen suoritusvaiheet sekä tutkielman laatimisessa noudatettavat periaatteet ja perehdytään tutkimuksessa käytettäviin tietolähteisiin.

The Master's thesis is the final project of the Master's degree, which demonstrates the student's knowledge of a topic of scientific or societal importance. The thesis is a research or an implementation project. A report is prepared following the instructions for the Master's thesis. The report contains description of the problem and the context, the used methods, describes the actual analysis and actions in the implementation, provides the results and evaluates the outcomes and conclusions.

Components of GPUs and their architectural differences affecting GPU computing. Low-level programming interfaces such as Compute unified device architecture (CUDA). Intermediate-level programming libraries with GPU acceleration. High-level frameworks for employing GPUs for solving computational problems. Project work focusing on a GPU-accelerated algorithm implemented using a selected abstraction level of programming and C++, Julia, Matlab or Python as the programming language.

The first part provides the skills defined in the aims of the course, including the skills to prepare and to give the seminar presentation in the second part. Independent preparation of a written seminar on a given data-centric engineering topic.

Algoritminen ongelmanratkaisu: johdatus tietojenkäsittelyyn, ongelmanratkaisu, algoritmien laatiminen, algoritmien suunnittelu, algoritmien kompleksisuus, hakuongelmat ja pelien pelaaminen. Tieto ja tiedon muuntaminen: tieto ja tiedon koodaus, informaatio ja tiedon tiivistäminen, tietorakenteet, tiedon salaus, propositilogiikka ja päättely sekä kääntäminen käytännössä.

Mechanics part of the course: Basics of translational and rotational motion, Newton's laws, principles of conservation of energy, momentum and angular momentum. Thermal Physics: Physical basics of thermodynamics, the laws of thermodynamics, thermodynamic engines and cyclic processes. Electricity: Electrostatics (electric force, field and potential), direct-current circuits, magnetism (magnetic force and field), electromagnetic induction.

The course introduces smart materials technology (adaptronics) that integrates actuator and sensor functions into materials and structures so that the adaptronic system can react to environmental stimuli. The goal is to create an intelligent and simple construction that replaces separate machine parts like semiconducting materials replaced separate electronic components. The course teaches how adaptronics can be miniaturized into micro- and nanoscales through the integration of separate functional components and how smart materials structures can be manufactured using 4D printing.

We study classical Microelectronics based on Silicon technology by considering p-n junctions, diodes, and transistors (bipolar junctions and MOSFET). The course includes also computations and simulations performed in MATLAB. These tasks help to visualize the working principle of devices and allow a better understanding of the lectures. We will also discuss the Moore's law and beyond.

The course begins by summarizing Maxwell equations for the electromagnetic field and the wave equations. Then the lectures discuss optical planar waveguides, linear optical fibres, propagation of linear pulses, LEDs, LASERs, detectors and photovoltaic devices. Some exercises with MATLAB will be given so that students can start their own numerical experiments.

Tieteellinen mittaustekniikka, tulostenkäsittely ja raportin teko.