In autonomous driving, scenario generation can play a critical role when it comes to the verification of the autonomous driving software. Since uncertainty is a major component in driving, there cannot be just one right answer to a prediction for the trajectory or the behaviour, and it becomes important to account for and model that uncertainty. Several approaches have been tried for generating the future scenarios for a vehicle and one such pioneering work set out to model the behaviour of the vehicles probabilistically while tackling the challenges of representation, flexibility, and transferability within one system. The proposed system is called the Semantic Graph Network (SGN) which utilizes feedforward neural networks, Gated Recurrent Units (GRU), and a generative model called the Mixed Density Network to serve its purpose. This thesis project set out in the direction of the implementation of this research work in the context of highway merger scenario and consists of three parts. The first part involves basic data analysis for the employed dataset, whereas the second part involves a model that implements certain parts of the SGN including a variation of the context encoding and the Mixture Density Network. The third and the final part is an attempt to recreate the SGN itself. While the first and the second parts were implemented successfully, for the third part, only certain objectives could be achieved. / Vid autonom körning kan scenariegenerering spela en avgörande roll när det gäller verifieringen av programvaran för autonom körning. Eftersom osäkerhet är en viktig komponent i körning kan det inte bara finnas ett rätt svar på en förutsägelse av banan eller beteendet, och det blir viktigt att redogöra för och modellera den osäkerheten. Flera tillvägagångssätt har prövats för att generera framtidsscenarierna för ett fordon och ett sådant banbrytande arbete gick ut på att modellera fordonens beteende sannolikt samtidigt som utmaningarna med representation, flexibilitet och överförbarhet inom ett system hanteras. Det föreslagna systemet kallas Semantic Graph Network (SGN) som använder neurala nätverk, Gated Recurrent Units (GRU) och en generativ modell som kallas Mixed Density Network för att tjäna sitt syfte. Detta examensarbete riktar sig mot genomförandet av detta forskningsarbete i samband med motorvägssammanslagningsscenariot och består av tre delar. Den första delen involverar grundläggande dataanalys för den använda datamängden, medan den andra delen involverar en modell som implementerar vissa delar av SGN inklusive en variation av kontextkodningen och Mixture Density Network. Den tredje och sista delen är ett försök att återskapa själva SGN. Även om den första och den andra delen genomfördes framgångsrikt, kunde endast vissa mål uppnås för den tredje delen.

Prediction of rock and fluid properties such as porosity, clay content, and water saturation is essential for exploration and development of hydrocarbon reservoirs. Rock and fluid property maps obtained from such predictions can be used for optimal selection of well locations for reservoir development and production enhancement. Seismic data are usually the only source of information available throughout a field that can be used to predict the 3D distribution of properties with appropriate spatial resolution. The main challenge in inferring properties from seismic data is the ambiguous nature of geophysical information. Therefore, any estimate of rock and fluid property maps derived from seismic data must also represent its associated uncertainty. In this study we develop a computationally efficient mathematical technique based on neural networks to integrate measured data and a priori information in order to reduce the uncertainty in rock and fluid properties in a reservoir. The post inversion (a posteriori) information about rock and fluid properties are represented by the joint probability density function (PDF) of porosity, clay content, and water saturation. In this technique the a posteriori PDF is modeled by a weighted sum of Gaussian PDF’s. A so-called mixture density network (MDN) estimates the weights, mean vector, and covariance matrix of the Gaussians given any measured data set. We solve several inverse problems with the MDN and compare results with Monte Carlo (MC) sampling solution and show that the MDN inversion technique provides good estimate of the MC sampling solution. However, the computational cost of training and using the neural network is much lower than solution found by MC sampling (more than a factor of 104 in some cases). We also discuss the design, implementation, and training procedure of the MDN, and its limitations in estimating the solution of an inverse problem. In this thesis we focus on data from a deep offshore field in Africa. Our goal is to apply the MDN inversion technique to obtain maps of petrophysical properties (i.e., porosity, clay content, water saturation), and petrophysical facies from 3D seismic data. Petrophysical facies (i.e., non-reservoir, oil- and brine-saturated reservoir facies) are defined probabilistically based on geological information and values of the petrophysical parameters. First, we investigate the relationship (i.e., petrophysical forward function) between compressional- and shear-wave velocity and petrophysical parameters. The petrophysical forward function depends on different properties of rocks and varies from one rock type to another. Therefore, after acquisition of well logs or seismic data from a geological setting the petrophysical forward function must be calibrated with data and observations. The uncertainty of the petrophysical forward function comes from uncertainty in measurements and uncertainty about the type of facies. We present a method to construct the petrophysical forward function with its associated uncertainty from the both sources above. The results show that introducing uncertainty in facies improves the accuracy of the petrophysical forward function predictions. Then, we apply the MDN inversion method to solve four different petrophysical inverse problems. In particular, we invert P- and S-wave impedance logs for the joint PDF of porosity, clay content, and water saturation using a calibrated petrophysical forward function. Results show that posterior PDF of the model parameters provides reasonable estimates of measured well logs. Errors in the posterior PDF are mainly due to errors in the petrophysical forward function. Finally, we apply the MDN inversion method to predict 3D petrophysical properties from attributes of seismic data. In this application, the inversion objective is to estimate the joint PDF of porosity, clay content, and water saturation at each point in the reservoir, from the compressional- and shear-wave-impedance obtained from the inversion of AVO seismic data. Uncertainty in the a posteriori PDF of the model parameters are due to different sources such as variations in effective pressure, bulk modulus and density of hydrocarbon, uncertainty of the petrophysical forward function, and random noise in recorded data. Results show that the standard deviations of all model parameters are reduced after inversion, which shows that the inversion process provides information about all parameters. We also applied the result of the petrophysical inversion to estimate the 3D probability maps of non-reservoir facies, brine- and oil-saturated reservoir facies. The accuracy of the predicted oil-saturated facies at the well location is good, but due to errors in the petrophysical inversion the predicted non-reservoir and brine-saturated facies are ambiguous. Although the accuracy of results may vary due to different sources of error in different applications, the fast, probabilistic method of solving non-linear inverse problems developed in this study can be applied to invert well logs and large seismic data sets for petrophysical parameters in different applications.

In recent years, machine learning has become utilized in external radiation therapy treatment planning. This involves automatic generation of treatment plans based on CT-scans and other spatial information such as the location of tumors and organs. The utility lies in relieving clinical staff from the labor of manually or semi-manually creating such plans. Rather than predicting a deterministic plan, there is great value in modeling it stochastically, i.e. predicting a probability distribution of dose from CT-scans and delineated biological structures. The stochasticity inherent in the RT treatment problem stems from the fact that a range of different plans can be adequate for a patient. The particular distribution can be thought of as the prevalence in preferences among clinicians. Having more information about the range of possible plans represented in one model entails that there is more flexibility in forming a final plan. Additionally, the model will be able to reflect the potentially conflicting clinical trade-offs; these will occur as multimodal distributions of dose in areas where there is a high variance. At RaySearch, the current method for doing this uses probabilistic random forests, an augmentation of the classical random forest algorithm. A current direction of research is learning the probability distribution using deep learning. A novel parametric approach to this is letting a suitable deep neural network approximate the parameters of a Gaussian mixture model in each volume element. Such a neural network is known as a mixture density network. This thesis establishes theoretical results of artificial neural networks, mainly the universal approximation theorem, applied to the activation functions used in the thesis. It will then proceed to investigate the power of deep learning in predicting dose distributions, both deterministically and stochastically. The primary objective is to investigate the feasibility of mixture density networks for stochastic prediction. The research question is the following. U-nets and Mixture Density Networks will be combined to predict stochastic doses. Does there exist such a network, powerful enough to detect and model bimodality? The experiments and investigations performed in this thesis demonstrate that there is indeed such a network. / Under de senaste åren har maskininlärning börjat nyttjas i extern strålbehandlingsplanering. Detta involverar automatisk generering av behandlingsplaner baserade på datortomografibilder och annan rumslig information, såsom placering av tumörer och organ. Nyttan ligger i att avlasta klinisk personal från arbetet med manuellt eller halvmanuellt skapa sådana planer. I stället för att predicera en deterministisk plan finns det stort värde att modellera den stokastiskt, det vill säga predicera en sannolikhetsfördelning av dos utifrån datortomografibilder och konturerade biologiska strukturer. Stokasticiteten som förekommer i strålterapibehandlingsproblemet beror på att en rad olika planer kan vara adekvata för en patient. Den särskilda fördelningen kan betraktas som förekomsten av preferenser bland klinisk personal. Att ha mer information om utbudet av möjliga planer representerat i en modell innebär att det finns mer flexibilitet i utformningen av en slutlig plan. Dessutom kommer modellen att kunna återspegla de potentiellt motstridiga kliniska avvägningarna; dessa kommer påträffas som multimodala fördelningar av dosen i områden där det finns en hög varians. På RaySearch används en probabilistisk random forest för att skapa dessa fördelningar, denna metod är en utökning av den klassiska random forest-algoritmen. En aktuell forskningsriktning är att generera in sannolikhetsfördelningen med hjälp av djupinlärning. Ett oprövat parametriskt tillvägagångssätt för detta är att låta ett lämpligt djupt neuralt nätverk approximera parametrarna för en Gaussisk mixturmodell i varje volymelement. Ett sådant neuralt nätverk är känt som ett mixturdensitetsnätverk. Den här uppsatsen fastställer teoretiska resultat för artificiella neurala nätverk, främst det universella approximationsteoremet, tillämpat på de aktiveringsfunktioner som används i uppsatsen. Den fortsätter sedan att utforska styrkan av djupinlärning i att predicera dosfördelningar, både deterministiskt och stokastiskt. Det primära målet är att undersöka lämpligheten av mixturdensitetsnätverk för stokastisk prediktion. Forskningsfrågan är följande. U-nets och mixturdensitetsnätverk kommer att kombineras för att predicera stokastiska doser. Finns det ett sådant nätverk som är tillräckligt kraftfullt för att upptäcka och modellera bimodalitet? Experimenten och undersökningarna som utförts i denna uppsats visar att det faktiskt finns ett sådant nätverk.