In the development of materials, the understanding of their properties is crucial. For magnetic materials, magnetism is an apparent property that needs to be accounted for. There are multiple factors explaining the phenomenon of magnetism, one being the effect of vibrations of the atoms on longitudinal spin fluctuations. This effect can be investigated by simulations, using density functional theory, and calculating energy landscapes. Through such simulations, the energy landscapes have been found to depend on the magnetic background and the positions of the atoms. However, when simulating a supercell of many atoms, to calculate energy landscapes for all atoms consumes many hours on the supercomputer. In this thesis, the possibility of using machine learning models to accelerate the approximation of energy landscapes is investigated. The material under investigation is body-centered cubic iron in the paramagnetic state at 1043 K. Machine learning enables statistical predictions to be made on new data based on patterns found in a previous set of data. Kernel ridge regression is used as the machine learning method. An important issue when training a machine learning model is the representation of the data in the so called descriptor (feature vector representation) or, more specific to this case, how the environment of an atom in a supercell is accounted for and represented properly. Four different descriptors are developed and compared to investigate which one yields the best result and why. Apart from comparing the descriptors, the results when using machine learning models are compared to when using other methods to approximate the energy landscapes. The machine learning models are also tested in a combined atomistic spin dynamics and ab initio molecular dynamics simulation (ASD-AIMD) where they were used to approximate energy landscapes and, from that, magnetic moment magnitudes at 1043 K. The results of these simulations are compared to the results from two other cases: one where the magnetic moment magnitudes are set to a constant value and one where they are set to their magnitudes at 0 K. From these investigations it is found that using machine learning methods to approximate the energy landscapes does, to a large degree, decrease the errors compared to the other approximation methods investigated. Some weaknesses of the respective descriptors were detected and if, in future work, these are accounted for, the errors have the potential of being lowered further.

The study of the instabilities in boiling water reactors is of significant importance to the safety withwhich they can be operated, as they can cause damage to the reactor posing risks to both equipmentand personnel. The instabilities that concern this paper are progressive growths in the oscillatingpower of boiling-water reactors. As thermal power is oscillatory is important to be able to identifywhether or not the power amplitude is stable. The main focus of this paper has been the development of a neural network estimator of these insta-bilities, fitting a non-linear model function to data by estimating it’s parameters. In doing this, theambition was to optimize the networks to the point that it can deliver near ”best-guess” estimationsof the parameters which define these instabilities, evaluating the usefulness of these networks whenapplied to problems like this. The goal was to design both MLP(Multi-Layer Perceptron) and SVR/KRR(Support Vector Regres-sion/Kernel Rigde Regression) networks and improve them to the point that they provide reliableand useful information about the waves in question. This goal was accomplished only in part asthe SVR/KRR networks proved to have some difficulty in ascertaining the phase shift of the waves.Overall, however, these networks prove very useful in this kind of task, succeeding with a reasonabledegree of confidence to calculating the different parameters of the waves studied.

There is a demand for decision support tools that can model the electricity markets and allows to forecast the hourly electricity price. Many different ap- proach such as artificial neural network or support vector regression are used in the literature. This thesis provides comparison of several different estima- tors under one settings using available data from Czech electricity market. The resulting comparison of over 5000 different estimators led to a selection of several best performing models. The role of historical weather data (temper- ature, dew point and humidity) is also assesed within the comparison and it was found that while the inclusion of weather data might lead to overfitting, it is beneficial under the right circumstances. The best performing approach was the Lasso regression estimated using modified Lars. 1

To assist technology advancements, it is important to continue the search for new materials. The stability of a crystal structures is closely connected to its formation energy. By calculating the formation energies of theoretical crystal structures it is possible to find new stable materials. However, the number of possible structures are so many that traditional methods relying on quantum mechanics, such as Density Functional Theory (DFT), require too much computational time to be viable in such a project. A presented alternative to such calculations is machine learning. Machine learning is an umbrella term for algorithms that can use information gained from one set of data to predict properties of new, similar data. Feature vector representations (descriptors) are used to present data in an appropriate manner to the machine. Thus far, no combination of machine learning method and feature vector representation has been established as general and accurate enough to be of practical use for accelerating the phase diagram calculations necessary for predicting material stability. It is important that the method predicts all types of structures equally well, regardless of stability, composition, or geometrical structure. In this thesis, the performances of different feature vector representations were compared to each other. The machine learning method used was primarily Kernel Ridge Regression, implemented in Python. The training and validation were performed on two different datasets and subsets of these. The representation which consistently yielded the lowest cross-validated error was a representation using the Voronoi tessellation of the structure by Ward et. al. [Phys. Rev. B 96, 024104 (2017)]. Following up was an experimental representation called the SLATM representation presented by Huang and von Lilienfeld [arXiv:1707.04146], which is partially based on the Radial Distribution Function. The Voronoi representation achieved an MAE of 0.16 eV/atom at 3534 training set size for one of the sets, and 0.28 eV/atom at 10086 training set size for the other set. The effect of separating linear and non-linear energy contributions was evaluated using the sinusoidal and Coulomb representations. The result was that separating these improved the error for small training set sizes, but the effect diminishes as the training set size increases. The results from this thesis implicate that further work is still required for machine learning to be used effectively in the search for new materials.

To address inefficiency, waste, and the negative consequences of electricity generation, companies and government entities are looking to behavioural change among residential consumers. To drive behavioural change, consumers need better feedback about their electricity consumption. A monthly or quarterly bill provides the consumer with almost no useful information about the relationship between their behaviours and their electricity consumption. Smart meters are now widely dispersed in developed countries and they are capable of providing electricity consumption readings at an hourly resolution, but this data is mostly used as a basis for billing and not as a tool to assist the consumer in reducing their consumption. One component required to deliver innovative feedback mechanisms is the capability to forecast hourly electricity consumption at the household scale. The work presented by this thesis is an evaluation of the effectiveness of a selection of kernel based machine learning methods at forecasting the hourly aggregate electricity consumption for different sized sets of households. The work of this thesis demonstrates that k-Nearest Neighbour Regression and Gaussian process Regression are the most accurate methods within the constraints of the problem considered. In addition to accuracy, the advantages and disadvantages of each machine learning method are evaluated, and a simple comparison of each algorithms computational performance is made. / För att ta itu med ineffektivitet, avfall, och de negativa konsekvenserna av elproduktion så vill företag och myndigheter se beteendeförändringar bland hushållskonsumenter. För att skapa beteendeförändringar så behöver konsumenterna bättre återkoppling när det gäller deras elförbrukning. Den nuvarande återkopplingen i en månads- eller kvartalsfaktura ger konsumenten nästan ingen användbar information om hur deras beteenden relaterar till deras konsumtion. Smarta mätare finns nu överallt i de utvecklade länderna och de kan ge en mängd information om bostäders konsumtion, men denna data används främst som underlag för fakturering och inte som ett verktyg för att hjälpa konsumenterna att minska sin konsumtion. En komponent som krävs för att leverera innovativa återkopplingsmekanismer är förmågan att förutse elförbrukningen på hushållsskala. Arbetet som presenteras i denna avhandling är en utvärdering av noggrannheten hos ett urval av kärnbaserad maskininlärningsmetoder för att förutse den sammanlagda förbrukningen för olika stora uppsättningar av hushåll. Arbetet i denna avhandling visar att "k-Nearest Neighbour Regression" och "Gaussian Process Regression" är de mest exakta metoder inom problemets begränsningar. Förutom noggrannhet, så görs en utvärdering av fördelar, nackdelar och prestanda hos varje maskininlärningsmetod.

In this project machine learning (ML) interatomic potentials are trained and used in molecular dynamics (MD) simulations to predict the physical properties of total energy, mean squared displacement (MSD) and specific heat capacity for systems of bulk Aluminium and Silicon. The interatomic potentials investigated are potentials trained using the ML models kernel ridge regression (KRR) and moment tensor potentials (MTPs). The simulations using these ML potentials are then compared with results obtained from ab-initio simulations using the gold standard method of density functional theory (DFT), as implemented in the Vienna ab-intio simulation package (VASP). The results show that the MTP simulations reach comparable accuracy compared to the DFT simulations for the properties total energy and MSD for Aluminium, with errors in the orders of magnitudes of meV and 10-5 Å2. Specific heat capacity is not reasonably replicated for Aluminium. The MTP simulations do not reasonably replicate the studied properties for the system of Silicon. The KRR models are implemented in the most direct way, and do not yield reasonably low errors even when trained on all available 10000 time steps of DFT training data. On the other hand, the MTPs require only to be trained on approximately 100 time steps to replicate the physical properties of Aluminium with accuracy comparable to DFT. After being trained on 100 time steps, the trained MTPs achieve mean absolute errors in the orders of magnitudes for the energy per atom and force magnitude predictions of 10-3 and 10-1 respectively for Aluminium, and 10-3 and 10-2 respectively for Silicon. At the same time, the MTP simulations require less core hours to simulate the same amount of time steps as the DFT simulations. In conclusion, MTPs could very likely play a role in accelerating both materials simulations themselves and subsequently the emergence of the data-driven materials design and informatics paradigm.