In this thesis, a deep learning-based surrogate model for predicting sea ice dynamics is developed that is capable of predicting linear kinematic features in a high-resolution setting. Predicting sea ice dynamics at high resolutions is critical for understanding climate patterns and enabling safe navigation in Arctic regions. Traditional continuum models based on the viscous-plastic rheology are computationally intensive when employed at high resolutions to capture linear kinematic features (LKFs), which are narrow zones of deformation in sea ice.

A supervised learning approach was adopted, focusing on convolutional neural network architectures, specifically the U-Net and a classic bottleneck model. Various loss functions were explored, including traditional metrics like the MSE and novel domain-specific functions such as the strain rate error (SRE), which incorporates physical knowledge of sea ice behaviour. The models were trained on a dataset generated from numerical simulations of sea ice dynamics on a 2 km grid.

The key findings indicate that the U-Net architecture combined with the MSE+SRE loss function outperforms other models. This architecture's depth and use of skip connections allow it to capture complex, multi-scale patterns inherent in sea ice dynamics. The integration of the SRE into the loss function significantly enhances the model's ability to predict LKFs, demonstrating the benefit of incorporating domain knowledge into machine learning models.

While the surrogate model effectively predicts LKFs for short-term forecasts up to approximately 5.5 hours (10 time steps), errors accumulate over longer periods, leading to significant errors after about 11 hours (20 time steps). However, the efficiency gain of this surrogate model is striking: the computation of 10 time steps can be done within a second, compared to the 30 minutes that traditional numerical methods need. The study also underscores the critical importance of training data selection and preparation in influencing model performance and generalisation capabilities.

In conclusion, this work demonstrates that a deep learning-based surrogate model, particularly utilising the U-Net architecture and the MSE+SRE loss function, can effectively predict sea ice dynamics at high resolutions with significant computational efficiency. The model generates forecasts within seconds, offering a viable alternative to traditional numerical simulations that require hours of computation. Future work should focus on mitigating error accumulation to extend the forecasting horizon and exploring advanced learning methods to further integrate physical insights into the modelling process.

In this thesis, an algorithm to model the magnetic perturbation field caused by ships is designed and implemented. A systematic description of methods used for modelling the magnetic signature of ships is given. The algorithm fits coefficients of a prolate spheroidal harmonic expansion of the scalar potential of the magnetic field using a least angle regression method (LARS) modified to implement Lasso regularisation. A Monte Carlo method with model selection based on Akaike's information criterion (AIC) is used to select optimal parameters specifying the prolate spheroidal coordinate system centred on the ship. Furthermore, a method to restrict the degree and order of the harmonic expansion is presented and an extension of the scikit-learn module in Python is given. The predictive power of the model was verified using simulated test data, which showed that the designed model is able to make adequate predictions, but improvements are needed. Different analyses on the inputs of the model showed that the model is succesful for low levels of noise, but is susceptible to overfitting for higher levels of noise. Several recommendations for further research are made.