Burn injuries occur daily and can have severe physical and mental effects both in short and long term, such as disabilities due to severe skin contraction. Even though the mortality rate has decreased over the years, the need for a higher quality of life after severe burns remains. Decreasing the probability of a severe contraction is essential for increasing the quality of life. Mathematical models have been developed to predict skin contraction over time. However, the computations are time-expensive and not suitable for applications that require many simulations, for example, when considering input uncertainty for patient-based predictions. To that end, the application of neural network surrogates is studied to accelerate the computations of a morphoelastic numerical model for the prediction of skin contraction. Two datasets are generated from a one- and two-dimensional model respectively and are used to train the neural networks. It is shown that a feedforward neural network can accurately learn the nonlinear mapping between the input parameters and the outputs of the considered morphoelastic models. The trained neural network provides fast and accurate predictions on skin contraction and strain energy. Furthermore, a first step is taken towards a hybrid model where a neural network is applied as a surrogate for computationally expensive time-stepping in the numerical model. The added value of fast neural network surrogates is demonstrated in two clinical case studies. It is shown that the surrogate can be used to perform input parameter studies by comparing an age study with the morphoelastic model with the age study using the neural network. The neural network can reproduce the age study with high accuracy in just a fraction of the time. Secondly, a concept application is designed to demonstrate patient-based predictions using Monte-Carlo simulations to cope with input parameter uncertainty. The application provides predictions for skin contraction and the strain energy, based on the age of the patient and the wound size.

This research presents a data-driven model for the magnetic signature of an object, consisting of linearly reacting isotropicmaterial. From magnetostatics mathematical-physical model is derived for the linear behaviour of the induced magnetization. Data-driven updates for the permanent magnetization are computed from comparisons of the computed magnetic field with measurements from onboard sensors, in order to describe magnetic hysteresis. In order to improve the solutions for ill-posed inverse problems, the Tikhonov regularization method is studied. Furthermore, the performance of the model is examined by a number of twin experiments.